linear_algebra.dual ⟷ Mathlib.LinearAlgebra.Dual

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -545,7 +545,7 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   by
   rw [ker_eq_bot']
   intro m hm
-  simp_rw [LinearMap.ext_iff, dual.eval_apply, zero_apply] at hm 
+  simp_rw [LinearMap.ext_iff, dual.eval_apply, zero_apply] at hm
   exact (Basis.forall_coord_eq_zero_iff _).mp fun i => hm (b.coord i)
 #align basis.eval_ker Basis.eval_ker
 -/
@@ -607,7 +607,7 @@ theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b :
   classical
   cases nonempty_fintype ι
   have := LinearEquiv.lift_rank_eq b.to_dual_equiv
-  simp only [Cardinal.lift_umax] at this 
+  simp only [Cardinal.lift_umax] at this
   rw [this, ← Cardinal.lift_umax]
   apply Cardinal.lift_id
 #align basis.dual_rank_eq Basis.dual_rank_eq
@@ -877,7 +877,7 @@ theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '
   intro i hi
   rcases(Finsupp.mem_span_image_iff_total _).mp hmem with ⟨l, supp_l, rfl⟩
   apply not_imp_comm.mp ((Finsupp.mem_supported' _ _).mp supp_l i)
-  rwa [← lc_def, h.dual_lc] at hi 
+  rwa [← lc_def, h.dual_lc] at hi
 #align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_span
 -/
 
@@ -979,7 +979,7 @@ theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Mo
       simp only [mem_dual_annihilator, mem_dual_coannihilator]
       intro y hy
       have := h hy
-      simp only [mem_dual_annihilator, mem_dual_coannihilator] at this 
+      simp only [mem_dual_annihilator, mem_dual_coannihilator] at this
       exact this x hx
 #align submodule.dual_annihilator_gc Submodule.dualAnnihilator_gc
 -/
@@ -1141,8 +1141,8 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
   obtain ⟨⟨w, w'⟩, rfl, -⟩ := exists_unique_add_of_is_compl_prod hW v
   have hw'n : (w' : V) ∉ W := by contrapose! hv; exact Submodule.add_mem W w.2 hv
   have hw'nz : w' ≠ 0 := by rintro rfl; exact hw'n (Submodule.zero_mem W)
-  rw [Ne.def, ← Module.forall_dual_apply_eq_zero_iff K w'] at hw'nz 
-  push_neg at hw'nz 
+  rw [Ne.def, ← Module.forall_dual_apply_eq_zero_iff K w'] at hw'nz
+  push_neg at hw'nz
   obtain ⟨φ, hφ⟩ := hw'nz
   exists ((LinearMap.ofIsComplProd hW).comp (LinearMap.inr _ _ _)) φ
   simp only [coe_comp, coe_inr, Function.comp_apply, of_is_compl_prod_apply, map_add,
@@ -1306,7 +1306,7 @@ theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
     W.dualAnnihilator.dualAnnihilator = Module.mapEvalEquiv K V W :=
   by
   have : _ = W := Subspace.dualAnnihilator_dualCoannihilator_eq
-  rw [dual_coannihilator, ← Module.mapEvalEquiv_symm_apply] at this 
+  rw [dual_coannihilator, ← Module.mapEvalEquiv_symm_apply] at this
   rwa [← OrderIso.symm_apply_eq]
 #align subspace.dual_annihilator_dual_annihilator_eq Subspace.dualAnnihilator_dualAnnihilator_eq
 -/
@@ -1375,13 +1375,13 @@ variable (f : M₁ →ₗ[R] M₂)
 theorem ker_dualMap_eq_dualAnnihilator_range : f.dualMap.ker = f.range.dualAnnihilator :=
   by
   ext φ; constructor <;> intro hφ
-  · rw [mem_ker] at hφ 
+  · rw [mem_ker] at hφ
     rw [Submodule.mem_dualAnnihilator]
     rintro y ⟨x, rfl⟩
     rw [← dual_map_apply, hφ, zero_apply]
   · ext x
     rw [dual_map_apply]
-    rw [Submodule.mem_dualAnnihilator] at hφ 
+    rw [Submodule.mem_dualAnnihilator] at hφ
     exact hφ (f x) ⟨x, rfl⟩
 #align linear_map.ker_dual_map_eq_dual_annihilator_range LinearMap.ker_dualMap_eq_dualAnnihilator_range
 -/
@@ -1716,7 +1716,7 @@ theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
   by
   have := Submodule.finrank_quotient_add_finrank f.range
   rw [(Subspace.quotEquivAnnihilator f.range).finrank_eq, ←
-    ker_dual_map_eq_dual_annihilator_range] at this 
+    ker_dual_map_eq_dual_annihilator_range] at this
   conv_rhs at this => rw [← Subspace.dual_finrank_eq]
   refine' add_left_injective (finrank K f.dual_map.ker) _
   change _ + _ = _ + _
@@ -1734,7 +1734,7 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
   rw [← range_eq_top, ← ker_eq_bot]
   intro h
   apply Submodule.eq_top_of_finrank_eq
-  rw [← Submodule.finrank_eq_zero] at h 
+  rw [← Submodule.finrank_eq_zero] at h
   rw [← add_zero (FiniteDimensional.finrank K f.range), ← h, ←
     LinearMap.finrank_range_dualMap_eq_finrank_range, LinearMap.finrank_range_add_finrank_ker,
     Subspace.dual_finrank_eq]

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1842,7 +1842,7 @@ noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N)
   by
   refine' LinearEquiv.ofLinear (dual_distrib R M N) (dual_distrib_inv_of_basis b c) _ _
   · ext f m n
-    have h : ∀ r s : R, r • s = s • r := IsCommutative.comm
+    have h : ∀ r s : R, r • s = s • r := Std.Commutative.comm
     simp only [compr₂_apply, mk_apply, comp_apply, id_apply, dual_distrib_inv_of_basis_apply,
       map_sum, map_smul, sum_apply, smul_apply, dual_distrib_apply, h (f _) _, ← f.map_smul, ←
       f.map_sum, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis, Basis.coord_apply,

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1669,7 +1669,7 @@ theorem dualAnnihilator_iInf_eq {ι : Type _} [Finite ι] (W : ι → Subspace K
   · intro α β h hyp W
     rw [← h.infi_comp, hyp (W ∘ h), ← h.supr_comp]
   · intro W
-    rw [iSup_of_empty', iInf_of_empty', sInf_empty, sSup_empty, dual_annihilator_top]
+    rw [iSup_of_empty', iInf_of_isEmpty, sInf_empty, sSup_empty, dual_annihilator_top]
   · intro α _ h W
     rw [iInf_option, iSup_option, dual_annihilator_inf_eq, h]
 #align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_iInf_eq

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -551,7 +551,11 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
 -/
 
 #print Basis.eval_range /-
-theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by classical
+theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by
+  classical
+  cases nonempty_fintype ι
+  rw [← b.to_dual_to_dual, range_comp, b.to_dual_range, Submodule.map_top, to_dual_range _]
+  infer_instance
 #align basis.eval_range Basis.eval_range
 -/
 
@@ -599,7 +603,13 @@ theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b :
 
 #print Basis.dual_rank_eq /-
 theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
-    Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by classical
+    Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by
+  classical
+  cases nonempty_fintype ι
+  have := LinearEquiv.lift_rank_eq b.to_dual_equiv
+  simp only [Cardinal.lift_umax] at this 
+  rw [this, ← Cardinal.lift_umax]
+  apply Cardinal.lift_id
 #align basis.dual_rank_eq Basis.dual_rank_eq
 -/
 
@@ -618,7 +628,7 @@ section
 variable (K) (V)
 
 #print Module.eval_ker /-
-theorem eval_ker : (eval K V).ker = ⊥ := by classical
+theorem eval_ker : (eval K V).ker = ⊥ := by classical exact (Basis.ofVectorSpace K V).eval_ker
 #align module.eval_ker Module.eval_ker
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -551,11 +551,7 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
 -/
 
 #print Basis.eval_range /-
-theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by
-  classical
-  cases nonempty_fintype ι
-  rw [← b.to_dual_to_dual, range_comp, b.to_dual_range, Submodule.map_top, to_dual_range _]
-  infer_instance
+theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by classical
 #align basis.eval_range Basis.eval_range
 -/
 
@@ -603,13 +599,7 @@ theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b :
 
 #print Basis.dual_rank_eq /-
 theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
-    Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by
-  classical
-  cases nonempty_fintype ι
-  have := LinearEquiv.lift_rank_eq b.to_dual_equiv
-  simp only [Cardinal.lift_umax] at this 
-  rw [this, ← Cardinal.lift_umax]
-  apply Cardinal.lift_id
+    Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by classical
 #align basis.dual_rank_eq Basis.dual_rank_eq
 -/
 
@@ -628,7 +618,7 @@ section
 variable (K) (V)
 
 #print Module.eval_ker /-
-theorem eval_ker : (eval K V).ker = ⊥ := by classical exact (Basis.ofVectorSpace K V).eval_ker
+theorem eval_ker : (eval K V).ker = ⊥ := by classical
 #align module.eval_ker Module.eval_ker
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1734,7 +1734,7 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
   rw [← range_eq_top, ← ker_eq_bot]
   intro h
   apply Submodule.eq_top_of_finrank_eq
-  rw [← finrank_eq_zero] at h 
+  rw [← Submodule.finrank_eq_zero] at h 
   rw [← add_zero (FiniteDimensional.finrank K f.range), ← h, ←
     LinearMap.finrank_range_dualMap_eq_finrank_range, LinearMap.finrank_range_add_finrank_ker,
     Subspace.dual_finrank_eq]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -339,7 +339,7 @@ theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0
 @[simp]
 theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total ι M R b f) (b i) = f i :=
   by
-  rw [Finsupp.total_apply, Finsupp.sum, LinearMap.map_sum, LinearMap.sum_apply]
+  rw [Finsupp.total_apply, Finsupp.sum, map_sum, LinearMap.sum_apply]
   simp_rw [LinearMap.map_smul, LinearMap.smul_apply, to_dual_apply, smul_eq_mul, mul_boole,
     Finset.sum_ite_eq']
   split_ifs with h
@@ -352,7 +352,7 @@ theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total 
 @[simp]
 theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.total ι M R b f) = f i :=
   by
-  rw [Finsupp.total_apply, Finsupp.sum, LinearMap.map_sum]
+  rw [Finsupp.total_apply, Finsupp.sum, map_sum]
   simp_rw [LinearMap.map_smul, to_dual_apply, smul_eq_mul, mul_boole, Finset.sum_ite_eq]
   split_ifs with h
   · rfl
@@ -818,7 +818,7 @@ variable [DecidableEq ι] (h : DualBases e ε)
 #print Module.DualBases.dual_lc /-
 theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i :=
   by
-  erw [LinearMap.map_sum]
+  erw [map_sum]
   simp only [h.eval, map_smul, smul_eq_mul]
   rw [Finset.sum_eq_single i]
   · simp
@@ -1844,9 +1844,9 @@ noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N)
   · ext f m n
     have h : ∀ r s : R, r • s = s • r := IsCommutative.comm
     simp only [compr₂_apply, mk_apply, comp_apply, id_apply, dual_distrib_inv_of_basis_apply,
-      LinearMap.map_sum, map_smul, sum_apply, smul_apply, dual_distrib_apply, h (f _) _, ←
-      f.map_smul, ← f.map_sum, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis,
-      Basis.coord_apply, Basis.sum_repr]
+      map_sum, map_smul, sum_apply, smul_apply, dual_distrib_apply, h (f _) _, ← f.map_smul, ←
+      f.map_sum, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis, Basis.coord_apply,
+      Basis.sum_repr]
   · ext f g
     simp only [compr₂_apply, mk_apply, comp_apply, id_apply, dual_distrib_inv_of_basis_apply,
       dual_distrib_apply, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis,

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,11 +3,11 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
 -/
-import Mathbin.LinearAlgebra.FiniteDimensional
-import Mathbin.LinearAlgebra.Projection
-import Mathbin.LinearAlgebra.SesquilinearForm
-import Mathbin.RingTheory.Finiteness
-import Mathbin.LinearAlgebra.FreeModule.Finite.Basic
+import LinearAlgebra.FiniteDimensional
+import LinearAlgebra.Projection
+import LinearAlgebra.SesquilinearForm
+import RingTheory.Finiteness
+import LinearAlgebra.FreeModule.Finite.Basic
 
 #align_import linear_algebra.dual from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 
@@ -747,7 +747,7 @@ variable {R M ι : Type _}
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
 -- TODO: In Lean 4 we can remove this and use `by { intros; exact Set.toFinite _ }` as a default
 -- argument.
 /-- Try using `set.to_finite` to dispatch a `set.finite` goal. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

@@ -1733,7 +1733,7 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
   refine' ⟨_, fun h => dual_map_injective_of_surjective h⟩
   rw [← range_eq_top, ← ker_eq_bot]
   intro h
-  apply FiniteDimensional.eq_top_of_finrank_eq
+  apply Submodule.eq_top_of_finrank_eq
   rw [← finrank_eq_zero] at h 
   rw [← add_zero (FiniteDimensional.finrank K f.range), ← h, ←
     LinearMap.finrank_range_dualMap_eq_finrank_range, LinearMap.finrank_range_add_finrank_ker,

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

@@ -559,20 +559,16 @@ theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).ran
 #align basis.eval_range Basis.eval_range
 -/
 
-#print Basis.evalEquiv /-
 /-- A module with a basis is linearly equivalent to the dual of its dual space. -/
 def evalEquiv {ι : Type _} [Finite ι] (b : Basis ι R M) : M ≃ₗ[R] Dual R (Dual R M) :=
   LinearEquiv.ofBijective (eval R M) ⟨ker_eq_bot.mp b.eval_ker, range_eq_top.mp b.eval_range⟩
 #align basis.eval_equiv Basis.evalEquiv
--/
 
-#print Basis.evalEquiv_toLinearMap /-
 @[simp]
 theorem evalEquiv_toLinearMap {ι : Type _} [Finite ι] (b : Basis ι R M) :
     b.evalEquiv.toLinearMap = Dual.eval R M :=
   rfl
 #align basis.eval_equiv_to_linear_map Basis.evalEquiv_toLinearMap
--/
 
 section
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
-
-! This file was ported from Lean 3 source module linear_algebra.dual
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.FiniteDimensional
 import Mathbin.LinearAlgebra.Projection
@@ -14,6 +9,8 @@ import Mathbin.LinearAlgebra.SesquilinearForm
 import Mathbin.RingTheory.Finiteness
 import Mathbin.LinearAlgebra.FreeModule.Finite.Basic
 
+#align_import linear_algebra.dual from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Dual vector spaces
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -521,7 +521,7 @@ theorem dualBasis_apply (i : ι) (m : M) : b.dualBasis i m = b.repr m i :=
 
 #print Basis.coe_dualBasis /-
 @[simp]
-theorem coe_dualBasis : ⇑b.dualBasis = b.Coord := by ext (i x); apply dual_basis_apply
+theorem coe_dualBasis : ⇑b.dualBasis = b.Coord := by ext i x; apply dual_basis_apply
 #align basis.coe_dual_basis Basis.coe_dualBasis
 -/
 
@@ -1227,7 +1227,7 @@ theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLi
 #print Subspace.dualRestrict_comp_dualLift /-
 @[simp]
 theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.dualLift = 1 := by
-  ext (φ x); simp
+  ext φ x; simp
 #align subspace.dual_restrict_comp_dual_lift Subspace.dualRestrict_comp_dualLift
 -/
 
@@ -1524,7 +1524,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
   · rw [LinearMap.range_comp_of_range_eq_top]
     apply LinearEquiv.range
   · apply congr_arg
-    ext (φ x)
+    ext φ x
     simp only [LinearMap.coe_comp, LinearEquiv.coe_toLinearMap, LinearMap.dualMap_apply,
       LinearEquiv.dualMap_apply, mkq_apply, f', LinearMap.quotKerEquivOfSurjective,
       LinearEquiv.trans_symm, LinearEquiv.trans_apply, LinearEquiv.ofTop_symm_apply,
@@ -1848,13 +1848,13 @@ noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N)
     Dual R M ⊗[R] Dual R N ≃ₗ[R] Dual R (M ⊗[R] N) :=
   by
   refine' LinearEquiv.ofLinear (dual_distrib R M N) (dual_distrib_inv_of_basis b c) _ _
-  · ext (f m n)
+  · ext f m n
     have h : ∀ r s : R, r • s = s • r := IsCommutative.comm
     simp only [compr₂_apply, mk_apply, comp_apply, id_apply, dual_distrib_inv_of_basis_apply,
       LinearMap.map_sum, map_smul, sum_apply, smul_apply, dual_distrib_apply, h (f _) _, ←
       f.map_smul, ← f.map_sum, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis,
       Basis.coord_apply, Basis.sum_repr]
-  · ext (f g)
+  · ext f g
     simp only [compr₂_apply, mk_apply, comp_apply, id_apply, dual_distrib_inv_of_basis_apply,
       dual_distrib_apply, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis,
       Basis.sum_dual_apply_smul_coord]

mathlib commit https://github.com/leanprover-community/mathlib/commit/893964fc28cefbcffc7cb784ed00a2895b4e65cf

@@ -1204,7 +1204,7 @@ theorem dualAnnihilator_inj {W W' : Subspace K V} :
 an arbitrary extension of `φ` to an element of the dual of `V`.
 That is, `dual_lift W φ` sends `w ∈ W` to `φ x` and `x` in a chosen complement of `W` to `0`. -/
 noncomputable def dualLift (W : Subspace K V) : Module.Dual K W →ₗ[K] Module.Dual K V :=
-  let h := Classical.indefiniteDescription _ W.exists_isCompl
+  let h := Classical.indefiniteDescription _ W.exists_is_compl
   (LinearMap.ofIsComplProd h.2).comp (LinearMap.inl _ _ _)
 #align subspace.dual_lift Subspace.dualLift
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -119,10 +119,12 @@ def dualPairing (R M) [CommSemiring R] [AddCommMonoid M] [Module R M] :
 #align module.dual_pairing Module.dualPairing
 -/
 
+#print Module.dualPairing_apply /-
 @[simp]
 theorem dualPairing_apply (v x) : dualPairing R M v x = v x :=
   rfl
 #align module.dual_pairing_apply Module.dualPairing_apply
+-/
 
 namespace Dual
 
@@ -140,10 +142,12 @@ def eval : M →ₗ[R] Dual R (Dual R M) :=
 #align module.dual.eval Module.Dual.eval
 -/
 
+#print Module.Dual.eval_apply /-
 @[simp]
 theorem eval_apply (v : M) (a : Dual R M) : eval R M v a = a v :=
   rfl
 #align module.dual.eval_apply Module.Dual.eval_apply
+-/
 
 variable {R M} {M' : Type _} [AddCommMonoid M'] [Module R M']
 
@@ -155,16 +159,20 @@ def transpose : (M →ₗ[R] M') →ₗ[R] Dual R M' →ₗ[R] Dual R M :=
 #align module.dual.transpose Module.Dual.transpose
 -/
 
+#print Module.Dual.transpose_apply /-
 theorem transpose_apply (u : M →ₗ[R] M') (l : Dual R M') : transpose u l = l.comp u :=
   rfl
 #align module.dual.transpose_apply Module.Dual.transpose_apply
+-/
 
 variable {M'' : Type _} [AddCommMonoid M''] [Module R M'']
 
+#print Module.Dual.transpose_comp /-
 theorem transpose_comp (u : M' →ₗ[R] M'') (v : M →ₗ[R] M') :
     transpose (u.comp v) = (transpose v).comp (transpose u) :=
   rfl
 #align module.dual.transpose_comp Module.Dual.transpose_comp
+-/
 
 end Dual
 
@@ -172,17 +180,21 @@ section Prod
 
 variable (M' : Type _) [AddCommMonoid M'] [Module R M']
 
+#print Module.dualProdDualEquivDual /-
 /-- Taking duals distributes over products. -/
 @[simps]
 def dualProdDualEquivDual : (Module.Dual R M × Module.Dual R M') ≃ₗ[R] Module.Dual R (M × M') :=
   LinearMap.coprodEquiv R
 #align module.dual_prod_dual_equiv_dual Module.dualProdDualEquivDual
+-/
 
+#print Module.dualProdDualEquivDual_apply /-
 @[simp]
 theorem dualProdDualEquivDual_apply (φ : Module.Dual R M) (ψ : Module.Dual R M') :
     dualProdDualEquivDual R M M' (φ, ψ) = φ.coprod ψ :=
   rfl
 #align module.dual_prod_dual_equiv_dual_apply Module.dualProdDualEquivDual_apply
+-/
 
 end Prod
 
@@ -204,19 +216,25 @@ def LinearMap.dualMap (f : M₁ →ₗ[R] M₂) : Dual R M₂ →ₗ[R] Dual R M
 #align linear_map.dual_map LinearMap.dualMap
 -/
 
+#print LinearMap.dualMap_def /-
 theorem LinearMap.dualMap_def (f : M₁ →ₗ[R] M₂) : f.dualMap = Module.Dual.transpose f :=
   rfl
 #align linear_map.dual_map_def LinearMap.dualMap_def
+-/
 
+#print LinearMap.dualMap_apply' /-
 theorem LinearMap.dualMap_apply' (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) : f.dualMap g = g.comp f :=
   rfl
 #align linear_map.dual_map_apply' LinearMap.dualMap_apply'
+-/
 
+#print LinearMap.dualMap_apply /-
 @[simp]
 theorem LinearMap.dualMap_apply (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
     f.dualMap g x = g (f x) :=
   rfl
 #align linear_map.dual_map_apply LinearMap.dualMap_apply
+-/
 
 #print LinearMap.dualMap_id /-
 @[simp]
@@ -224,11 +242,14 @@ theorem LinearMap.dualMap_id : (LinearMap.id : M₁ →ₗ[R] M₁).dualMap = Li
 #align linear_map.dual_map_id LinearMap.dualMap_id
 -/
 
+#print LinearMap.dualMap_comp_dualMap /-
 theorem LinearMap.dualMap_comp_dualMap {M₃ : Type _} [AddCommGroup M₃] [Module R M₃]
     (f : M₁ →ₗ[R] M₂) (g : M₂ →ₗ[R] M₃) : f.dualMap.comp g.dualMap = (g.comp f).dualMap :=
   rfl
 #align linear_map.dual_map_comp_dual_map LinearMap.dualMap_comp_dualMap
+-/
 
+#print LinearMap.dualMap_injective_of_surjective /-
 /-- If a linear map is surjective, then its dual is injective. -/
 theorem LinearMap.dualMap_injective_of_surjective {f : M₁ →ₗ[R] M₂} (hf : Function.Surjective f) :
     Function.Injective f.dualMap := by
@@ -237,6 +258,7 @@ theorem LinearMap.dualMap_injective_of_surjective {f : M₁ →ₗ[R] M₂} (hf
   obtain ⟨y, rfl⟩ := hf x
   exact congr_arg (fun g : Module.Dual R M₁ => g y) h
 #align linear_map.dual_map_injective_of_surjective LinearMap.dualMap_injective_of_surjective
+-/
 
 #print LinearEquiv.dualMap /-
 /-- The `linear_equiv` version of `linear_map.dual_map`. -/
@@ -254,11 +276,13 @@ def LinearEquiv.dualMap (f : M₁ ≃ₗ[R] M₂) : Dual R M₂ ≃ₗ[R] Dual R
 #align linear_equiv.dual_map LinearEquiv.dualMap
 -/
 
+#print LinearEquiv.dualMap_apply /-
 @[simp]
 theorem LinearEquiv.dualMap_apply (f : M₁ ≃ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
     f.dualMap g x = g (f x) :=
   rfl
 #align linear_equiv.dual_map_apply LinearEquiv.dualMap_apply
+-/
 
 #print LinearEquiv.dualMap_refl /-
 @[simp]
@@ -275,10 +299,12 @@ theorem LinearEquiv.dualMap_symm {f : M₁ ≃ₗ[R] M₂} :
 #align linear_equiv.dual_map_symm LinearEquiv.dualMap_symm
 -/
 
+#print LinearEquiv.dualMap_trans /-
 theorem LinearEquiv.dualMap_trans {M₃ : Type _} [AddCommGroup M₃] [Module R M₃] (f : M₁ ≃ₗ[R] M₂)
     (g : M₂ ≃ₗ[R] M₃) : g.dualMap.trans f.dualMap = (f.trans g).dualMap :=
   rfl
 #align linear_equiv.dual_map_trans LinearEquiv.dualMap_trans
+-/
 
 end DualMap
 
@@ -306,10 +332,13 @@ def toDual : M →ₗ[R] Module.Dual R M :=
 #align basis.to_dual Basis.toDual
 -/
 
+#print Basis.toDual_apply /-
 theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0 := by
   erw [constr_basis b, constr_basis b]; ac_rfl
 #align basis.to_dual_apply Basis.toDual_apply
+-/
 
+#print Basis.toDual_total_left /-
 @[simp]
 theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total ι M R b f) (b i) = f i :=
   by
@@ -320,7 +349,9 @@ theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total 
   · rfl
   · rw [finsupp.not_mem_support_iff.mp h]
 #align basis.to_dual_total_left Basis.toDual_total_left
+-/
 
+#print Basis.toDual_total_right /-
 @[simp]
 theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.total ι M R b f) = f i :=
   by
@@ -330,17 +361,24 @@ theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.
   · rfl
   · rw [finsupp.not_mem_support_iff.mp h]
 #align basis.to_dual_total_right Basis.toDual_total_right
+-/
 
+#print Basis.toDual_apply_left /-
 theorem toDual_apply_left (m : M) (i : ι) : b.toDual m (b i) = b.repr m i := by
   rw [← b.to_dual_total_left, b.total_repr]
 #align basis.to_dual_apply_left Basis.toDual_apply_left
+-/
 
+#print Basis.toDual_apply_right /-
 theorem toDual_apply_right (i : ι) (m : M) : b.toDual (b i) m = b.repr m i := by
   rw [← b.to_dual_total_right, b.total_repr]
 #align basis.to_dual_apply_right Basis.toDual_apply_right
+-/
 
+#print Basis.coe_toDual_self /-
 theorem coe_toDual_self (i : ι) : b.toDual (b i) = b.Coord i := by ext; apply to_dual_apply_right
 #align basis.coe_to_dual_self Basis.coe_toDual_self
+-/
 
 #print Basis.toDualFlip /-
 /-- `h.to_dual_flip v` is the linear map sending `w` to `h.to_dual w v`. -/
@@ -349,18 +387,25 @@ def toDualFlip (m : M) : M →ₗ[R] R :=
 #align basis.to_dual_flip Basis.toDualFlip
 -/
 
+#print Basis.toDualFlip_apply /-
 theorem toDualFlip_apply (m₁ m₂ : M) : b.toDualFlip m₁ m₂ = b.toDual m₂ m₁ :=
   rfl
 #align basis.to_dual_flip_apply Basis.toDualFlip_apply
+-/
 
+#print Basis.toDual_eq_repr /-
 theorem toDual_eq_repr (m : M) (i : ι) : b.toDual m (b i) = b.repr m i :=
   b.toDual_apply_left m i
 #align basis.to_dual_eq_repr Basis.toDual_eq_repr
+-/
 
+#print Basis.toDual_eq_equivFun /-
 theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.equivFun m i := by
   rw [b.equiv_fun_apply, to_dual_eq_repr]
 #align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFun
+-/
 
+#print Basis.toDual_inj /-
 theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   by
   rw [← mem_bot R, ← b.repr.ker, mem_ker, LinearEquiv.coe_coe]
@@ -369,11 +414,15 @@ theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   rw [← to_dual_eq_repr, a]
   rfl
 #align basis.to_dual_inj Basis.toDual_inj
+-/
 
+#print Basis.toDual_ker /-
 theorem toDual_ker : b.toDual.ker = ⊥ :=
   ker_eq_bot'.mpr b.toDual_inj
 #align basis.to_dual_ker Basis.toDual_ker
+-/
 
+#print Basis.toDual_range /-
 theorem toDual_range [Finite ι] : b.toDual.range = ⊤ :=
   by
   cases nonempty_fintype ι
@@ -384,6 +433,7 @@ theorem toDual_range [Finite ι] : b.toDual.range = ⊤ :=
   rw [b.to_dual_eq_repr _ i, repr_total b]
   rfl
 #align basis.to_dual_range Basis.toDual_range
+-/
 
 end CommSemiring
 
@@ -422,11 +472,13 @@ def toDualEquiv : M ≃ₗ[R] Dual R M :=
 #align basis.to_dual_equiv Basis.toDualEquiv
 -/
 
+#print Basis.toDualEquiv_apply /-
 -- `simps` times out when generating this
 @[simp]
 theorem toDualEquiv_apply (m : M) : b.toDualEquiv m = b.toDual m :=
   rfl
 #align basis.to_dual_equiv_apply Basis.toDualEquiv_apply
+-/
 
 #print Basis.dualBasis /-
 /-- Maps a basis for `V` to a basis for the dual space. -/
@@ -435,11 +487,14 @@ def dualBasis : Basis ι R (Dual R M) :=
 #align basis.dual_basis Basis.dualBasis
 -/
 
+#print Basis.dualBasis_apply_self /-
 -- We use `j = i` to match `basis.repr_self`
 theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1 else 0 := by
   convert b.to_dual_apply i j using 2; rw [@eq_comm _ j i]
 #align basis.dual_basis_apply_self Basis.dualBasis_apply_self
+-/
 
+#print Basis.total_dualBasis /-
 theorem total_dualBasis (f : ι →₀ R) (i : ι) :
     Finsupp.total ι (Dual R M) R b.dualBasis f (b i) = f i :=
   by
@@ -450,14 +505,19 @@ theorem total_dualBasis (f : ι →₀ R) (i : ι) :
       if_pos (Finset.mem_univ i)]
   · intro; rw [zero_smul]
 #align basis.total_dual_basis Basis.total_dualBasis
+-/
 
+#print Basis.dualBasis_repr /-
 theorem dualBasis_repr (l : Dual R M) (i : ι) : b.dualBasis.repr l i = l (b i) := by
   rw [← total_dual_basis b, Basis.total_repr b.dual_basis l]
 #align basis.dual_basis_repr Basis.dualBasis_repr
+-/
 
+#print Basis.dualBasis_apply /-
 theorem dualBasis_apply (i : ι) (m : M) : b.dualBasis i m = b.repr m i :=
   b.toDual_apply_right i m
 #align basis.dual_basis_apply Basis.dualBasis_apply
+-/
 
 #print Basis.coe_dualBasis /-
 @[simp]
@@ -477,10 +537,13 @@ theorem toDual_toDual : b.dualBasis.toDual.comp b.toDual = Dual.eval R M :=
 
 end Finite
 
+#print Basis.dualBasis_equivFun /-
 theorem dualBasis_equivFun [Fintype ι] (l : Dual R M) (i : ι) :
     b.dualBasis.equivFun l i = l (b i) := by rw [Basis.equivFun_apply, dual_basis_repr]
 #align basis.dual_basis_equiv_fun Basis.dualBasis_equivFun
+-/
 
+#print Basis.eval_ker /-
 theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   by
   rw [ker_eq_bot']
@@ -488,13 +551,16 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   simp_rw [LinearMap.ext_iff, dual.eval_apply, zero_apply] at hm 
   exact (Basis.forall_coord_eq_zero_iff _).mp fun i => hm (b.coord i)
 #align basis.eval_ker Basis.eval_ker
+-/
 
+#print Basis.eval_range /-
 theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by
   classical
   cases nonempty_fintype ι
   rw [← b.to_dual_to_dual, range_comp, b.to_dual_range, Submodule.map_top, to_dual_range _]
   infer_instance
 #align basis.eval_range Basis.eval_range
+-/
 
 #print Basis.evalEquiv /-
 /-- A module with a basis is linearly equivalent to the dual of its dual space. -/
@@ -503,11 +569,13 @@ def evalEquiv {ι : Type _} [Finite ι] (b : Basis ι R M) : M ≃ₗ[R] Dual R
 #align basis.eval_equiv Basis.evalEquiv
 -/
 
+#print Basis.evalEquiv_toLinearMap /-
 @[simp]
 theorem evalEquiv_toLinearMap {ι : Type _} [Finite ι] (b : Basis ι R M) :
     b.evalEquiv.toLinearMap = Dual.eval R M :=
   rfl
 #align basis.eval_equiv_to_linear_map Basis.evalEquiv_toLinearMap
+-/
 
 section
 
@@ -531,13 +599,16 @@ end
 
 end CommRing
 
+#print Basis.total_coord /-
 /-- `simp` normal form version of `total_dual_basis` -/
 @[simp]
 theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b : Basis ι R M)
     (f : ι →₀ R) (i : ι) : Finsupp.total ι (Dual R M) R b.Coord f (b i) = f i := by
   haveI := Classical.decEq ι; rw [← coe_dual_basis, total_dual_basis]
 #align basis.total_coord Basis.total_coord
+-/
 
+#print Basis.dual_rank_eq /-
 theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
     Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by
   classical
@@ -547,6 +618,7 @@ theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b :
   rw [this, ← Cardinal.lift_umax]
   apply Cardinal.lift_id
 #align basis.dual_rank_eq Basis.dual_rank_eq
+-/
 
 end Basis
 
@@ -562,8 +634,10 @@ section
 
 variable (K) (V)
 
+#print Module.eval_ker /-
 theorem eval_ker : (eval K V).ker = ⊥ := by classical exact (Basis.ofVectorSpace K V).eval_ker
 #align module.eval_ker Module.eval_ker
+-/
 
 #print Module.map_eval_injective /-
 theorem map_eval_injective : (Submodule.map (eval K V)).Injective :=
@@ -591,17 +665,23 @@ section
 
 variable (K)
 
+#print Module.eval_apply_eq_zero_iff /-
 theorem eval_apply_eq_zero_iff (v : V) : (eval K V) v = 0 ↔ v = 0 := by
   simpa only using set_like.ext_iff.mp (eval_ker K V) v
 #align module.eval_apply_eq_zero_iff Module.eval_apply_eq_zero_iff
+-/
 
+#print Module.eval_apply_injective /-
 theorem eval_apply_injective : Function.Injective (eval K V) :=
   (injective_iff_map_eq_zero' (eval K V)).mpr (eval_apply_eq_zero_iff K)
 #align module.eval_apply_injective Module.eval_apply_injective
+-/
 
+#print Module.forall_dual_apply_eq_zero_iff /-
 theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v = 0) ↔ v = 0 := by
   rw [← eval_apply_eq_zero_iff K v, LinearMap.ext_iff]; rfl
 #align module.forall_dual_apply_eq_zero_iff Module.forall_dual_apply_eq_zero_iff
+-/
 
 end
 
@@ -613,10 +693,12 @@ theorem dual_rank_eq [FiniteDimensional K V] :
 #align module.dual_rank_eq Module.dual_rank_eq
 -/
 
+#print Module.erange_coe /-
 theorem erange_coe [FiniteDimensional K V] : (eval K V).range = ⊤ :=
   letI : IsNoetherian K V := IsNoetherian.iff_fg.2 inferInstance
   (Basis.ofVectorSpace K V).eval_range
 #align module.erange_coe Module.erange_coe
+-/
 
 variable (K V)
 
@@ -646,17 +728,21 @@ theorem evalEquiv_toLinearMap [FiniteDimensional K V] :
 #align module.eval_equiv_to_linear_map Module.evalEquiv_toLinearMap
 -/
 
+#print Module.mapEvalEquiv_apply /-
 @[simp]
 theorem mapEvalEquiv_apply [FiniteDimensional K V] (W : Subspace K V) :
     mapEvalEquiv K V W = W.map (eval K V) :=
   rfl
 #align module.map_eval_equiv_apply Module.mapEvalEquiv_apply
+-/
 
+#print Module.mapEvalEquiv_symm_apply /-
 @[simp]
 theorem mapEvalEquiv_symm_apply [FiniteDimensional K V] (W'' : Subspace K (Dual K (Dual K V))) :
     (mapEvalEquiv K V).symm W'' = W''.comap (eval K V) :=
   rfl
 #align module.map_eval_equiv_symm_apply Module.mapEvalEquiv_symm_apply
+-/
 
 end Module
 
@@ -701,6 +787,7 @@ variable [CommRing R] [AddCommGroup M] [Module R M]
 
 variable {e : ι → M} {ε : ι → Dual R M}
 
+#print Module.DualBases.coeffs /-
 /-- The coefficients of `v` on the basis `e` -/
 def coeffs [DecidableEq ι] (h : DualBases e ε) (m : M) : ι →₀ R
     where
@@ -708,28 +795,34 @@ def coeffs [DecidableEq ι] (h : DualBases e ε) (m : M) : ι →₀ R
   support := (h.Finite m).toFinset
   mem_support_toFun := by intro i; rw [Set.Finite.mem_toFinset, Set.mem_setOf_eq]
 #align module.dual_bases.coeffs Module.DualBases.coeffs
+-/
 
+#print Module.DualBases.coeffs_apply /-
 @[simp]
 theorem coeffs_apply [DecidableEq ι] (h : DualBases e ε) (m : M) (i : ι) : h.coeffs m i = ε i m :=
   rfl
 #align module.dual_bases.coeffs_apply Module.DualBases.coeffs_apply
+-/
 
+#print Module.DualBases.lc /-
 /-- linear combinations of elements of `e`.
 This is a convenient abbreviation for `finsupp.total _ M R e l` -/
 def lc {ι} (e : ι → M) (l : ι →₀ R) : M :=
   l.Sum fun (i : ι) (a : R) => a • e i
 #align module.dual_bases.lc Module.DualBases.lc
+-/
 
+#print Module.DualBases.lc_def /-
 theorem lc_def (e : ι → M) (l : ι →₀ R) : lc e l = Finsupp.total _ _ _ e l :=
   rfl
 #align module.dual_bases.lc_def Module.DualBases.lc_def
+-/
 
 open Module
 
 variable [DecidableEq ι] (h : DualBases e ε)
 
-include h
-
+#print Module.DualBases.dual_lc /-
 theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i :=
   by
   erw [LinearMap.map_sum]
@@ -741,12 +834,16 @@ theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i :=
   · intro p_not_in
     simp [Finsupp.not_mem_support_iff.1 p_not_in]
 #align module.dual_bases.dual_lc Module.DualBases.dual_lc
+-/
 
+#print Module.DualBases.coeffs_lc /-
 @[simp]
 theorem coeffs_lc (l : ι →₀ R) : h.coeffs (DualBases.lc e l) = l := by ext i;
   rw [h.coeffs_apply, h.dual_lc]
 #align module.dual_bases.coeffs_lc Module.DualBases.coeffs_lc
+-/
 
+#print Module.DualBases.lc_coeffs /-
 /-- For any m : M n, \sum_{p ∈ Q n} (ε p m) • e p = m -/
 @[simp]
 theorem lc_coeffs (m : M) : DualBases.lc e (h.coeffs m) = m :=
@@ -755,6 +852,7 @@ theorem lc_coeffs (m : M) : DualBases.lc e (h.coeffs m) = m :=
   intro i
   simp [-sub_eq_add_neg, LinearMap.map_sub, h.dual_lc, sub_eq_zero]
 #align module.dual_bases.lc_coeffs Module.DualBases.lc_coeffs
+-/
 
 #print Module.DualBases.basis /-
 /-- `(h : dual_bases e ε).basis` shows the family of vectors `e` forms a basis. -/
@@ -770,13 +868,16 @@ def basis : Basis ι R M :=
 #align module.dual_bases.basis Module.DualBases.basis
 -/
 
+#print Module.DualBases.coe_basis /-
 @[simp]
 theorem coe_basis : ⇑h.Basis = e := by
   ext i; rw [Basis.apply_eq_iff]; ext j
   rw [h.basis_repr_apply, coeffs_apply, h.eval, Finsupp.single_apply]
   convert if_congr eq_comm rfl rfl
 #align module.dual_bases.coe_basis Module.DualBases.coe_basis
+-/
 
+#print Module.DualBases.mem_of_mem_span /-
 -- `convert` to get rid of a `decidable_eq` mismatch
 theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '' H)) :
     ∀ i : ι, ε i x ≠ 0 → i ∈ H := by
@@ -785,12 +886,15 @@ theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '
   apply not_imp_comm.mp ((Finsupp.mem_supported' _ _).mp supp_l i)
   rwa [← lc_def, h.dual_lc] at hi 
 #align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_span
+-/
 
+#print Module.DualBases.coe_dualBasis /-
 theorem coe_dualBasis [Fintype ι] : ⇑h.Basis.dualBasis = ε :=
   funext fun i =>
     h.Basis.ext fun j => by
       rw [h.basis.dual_basis_apply_self, h.coe_basis, h.eval, if_congr eq_comm rfl rfl]
 #align module.dual_bases.coe_dual_basis Module.DualBases.coe_dualBasis
+-/
 
 end Module.DualBases
 
@@ -817,11 +921,13 @@ theorem dualRestrict_def (W : Submodule R M) : W.dualRestrict = W.Subtype.dualMa
 #align submodule.dual_restrict_def Submodule.dualRestrict_def
 -/
 
+#print Submodule.dualRestrict_apply /-
 @[simp]
 theorem dualRestrict_apply (W : Submodule R M) (φ : Module.Dual R M) (x : W) :
     W.dualRestrict φ x = φ (x : M) :=
   rfl
 #align submodule.dual_restrict_apply Submodule.dualRestrict_apply
+-/
 
 #print Submodule.dualAnnihilator /-
 /-- The `dual_annihilator` of a submodule `W` is the set of linear maps `φ` such
@@ -832,6 +938,7 @@ def dualAnnihilator {R : Type u} {M : Type v} [CommSemiring R] [AddCommMonoid M]
 #align submodule.dual_annihilator Submodule.dualAnnihilator
 -/
 
+#print Submodule.mem_dualAnnihilator /-
 @[simp]
 theorem mem_dualAnnihilator (φ : Module.Dual R M) : φ ∈ W.dualAnnihilator ↔ ∀ w ∈ W, φ w = 0 :=
   by
@@ -839,6 +946,7 @@ theorem mem_dualAnnihilator (φ : Module.Dual R M) : φ ∈ W.dualAnnihilator 
   simp_rw [LinearMap.ext_iff, dual_restrict_apply]
   exact ⟨fun h w hw => h ⟨w, hw⟩, fun h w => h w.1 w.2⟩
 #align submodule.mem_dual_annihilator Submodule.mem_dualAnnihilator
+-/
 
 #print Submodule.dualRestrict_ker_eq_dualAnnihilator /-
 /-- That $\operatorname{ker}(\iota^* : V^* \to W^*) = \operatorname{ann}(W)$.
@@ -857,11 +965,14 @@ def dualCoannihilator (Φ : Submodule R (Module.Dual R M)) : Submodule R M :=
 #align submodule.dual_coannihilator Submodule.dualCoannihilator
 -/
 
+#print Submodule.mem_dualCoannihilator /-
 theorem mem_dualCoannihilator {Φ : Submodule R (Module.Dual R M)} (x : M) :
     x ∈ Φ.dualCoannihilator ↔ ∀ φ ∈ Φ, (φ x : R) = 0 := by
   simp_rw [dual_coannihilator, mem_comap, mem_dual_annihilator, Module.Dual.eval_apply]
 #align submodule.mem_dual_coannihilator Submodule.mem_dualCoannihilator
+-/
 
+#print Submodule.dualAnnihilator_gc /-
 theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Module R M] :
     GaloisConnection
       (OrderDual.toDual ∘ (dualAnnihilator : Submodule R M → Submodule R (Module.Dual R M)))
@@ -878,6 +989,7 @@ theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Mo
       simp only [mem_dual_annihilator, mem_dual_coannihilator] at this 
       exact this x hx
 #align submodule.dual_annihilator_gc Submodule.dualAnnihilator_gc
+-/
 
 #print Submodule.le_dualAnnihilator_iff_le_dualCoannihilator /-
 theorem le_dualAnnihilator_iff_le_dualCoannihilator {U : Submodule R (Module.Dual R M)}
@@ -886,11 +998,14 @@ theorem le_dualAnnihilator_iff_le_dualCoannihilator {U : Submodule R (Module.Dua
 #align submodule.le_dual_annihilator_iff_le_dual_coannihilator Submodule.le_dualAnnihilator_iff_le_dualCoannihilator
 -/
 
+#print Submodule.dualAnnihilator_bot /-
 @[simp]
 theorem dualAnnihilator_bot : (⊥ : Submodule R M).dualAnnihilator = ⊤ :=
   (dualAnnihilator_gc R M).l_bot
 #align submodule.dual_annihilator_bot Submodule.dualAnnihilator_bot
+-/
 
+#print Submodule.dualAnnihilator_top /-
 @[simp]
 theorem dualAnnihilator_top : (⊤ : Submodule R M).dualAnnihilator = ⊥ :=
   by
@@ -899,11 +1014,14 @@ theorem dualAnnihilator_top : (⊤ : Submodule R M).dualAnnihilator = ⊥ :=
   simp_rw [mem_dual_annihilator, mem_bot, mem_top, forall_true_left]
   exact fun h => LinearMap.ext h
 #align submodule.dual_annihilator_top Submodule.dualAnnihilator_top
+-/
 
+#print Submodule.dualCoannihilator_bot /-
 @[simp]
 theorem dualCoannihilator_bot : (⊥ : Submodule R (Module.Dual R M)).dualCoannihilator = ⊤ :=
   (dualAnnihilator_gc R M).u_top
 #align submodule.dual_coannihilator_bot Submodule.dualCoannihilator_bot
+-/
 
 #print Submodule.dualAnnihilator_anti /-
 @[mono]
@@ -949,26 +1067,35 @@ theorem dualCoannihilator_dualAnnihilator_dualCoannihilator (U : Submodule R (Mo
 #align submodule.dual_coannihilator_dual_annihilator_dual_coannihilator Submodule.dualCoannihilator_dualAnnihilator_dualCoannihilator
 -/
 
+#print Submodule.dualAnnihilator_sup_eq /-
 theorem dualAnnihilator_sup_eq (U V : Submodule R M) :
     (U ⊔ V).dualAnnihilator = U.dualAnnihilator ⊓ V.dualAnnihilator :=
   (dualAnnihilator_gc R M).l_sup
 #align submodule.dual_annihilator_sup_eq Submodule.dualAnnihilator_sup_eq
+-/
 
+#print Submodule.dualCoannihilator_sup_eq /-
 theorem dualCoannihilator_sup_eq (U V : Submodule R (Module.Dual R M)) :
     (U ⊔ V).dualCoannihilator = U.dualCoannihilator ⊓ V.dualCoannihilator :=
   (dualAnnihilator_gc R M).u_inf
 #align submodule.dual_coannihilator_sup_eq Submodule.dualCoannihilator_sup_eq
+-/
 
+#print Submodule.dualAnnihilator_iSup_eq /-
 theorem dualAnnihilator_iSup_eq {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, U i).dualAnnihilator = ⨅ i : ι, (U i).dualAnnihilator :=
   (dualAnnihilator_gc R M).l_iSup
 #align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eq
+-/
 
+#print Submodule.dualCoannihilator_iSup_eq /-
 theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.Dual R M)) :
     (⨆ i : ι, U i).dualCoannihilator = ⨅ i : ι, (U i).dualCoannihilator :=
   (dualAnnihilator_gc R M).u_iInf
 #align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
+-/
 
+#print Submodule.sup_dualAnnihilator_le_inf /-
 /-- See also `subspace.dual_annihilator_inf_eq` for vector subspaces. -/
 theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
     U.dualAnnihilator ⊔ V.dualAnnihilator ≤ (U ⊓ V).dualAnnihilator :=
@@ -976,7 +1103,9 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
   rw [le_dual_annihilator_iff_le_dual_coannihilator, dual_coannihilator_sup_eq]
   apply inf_le_inf <;> exact le_dual_annihilator_dual_coannihilator _
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
+-/
 
+#print Submodule.iSup_dualAnnihilator_le_iInf /-
 /-- See also `subspace.dual_annihilator_infi_eq` for vector subspaces when `ι` is finite. -/
 theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, (U i).dualAnnihilator) ≤ (⨅ i : ι, U i).dualAnnihilator :=
@@ -985,6 +1114,7 @@ theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
   apply iInf_mono
   exact fun i : ι => le_dual_annihilator_dual_coannihilator (U i)
 #align submodule.supr_dual_annihilator_le_infi Submodule.iSup_dualAnnihilator_le_iInf
+-/
 
 end Submodule
 
@@ -997,11 +1127,13 @@ universe u v w
 -- We work in vector spaces because `exists_is_compl` only hold for vector spaces
 variable {K : Type u} {V : Type v} [Field K] [AddCommGroup V] [Module K V]
 
+#print Subspace.dualCoannihilator_top /-
 @[simp]
 theorem dualCoannihilator_top (W : Subspace K V) :
     (⊤ : Subspace K (Module.Dual K W)).dualCoannihilator = ⊥ := by
   rw [dual_coannihilator, dual_annihilator_top, comap_bot, Module.eval_ker]
 #align subspace.dual_coannihilator_top Subspace.dualCoannihilator_top
+-/
 
 #print Subspace.dualAnnihilator_dualCoannihilator_eq /-
 theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
@@ -1028,11 +1160,13 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
 #align subspace.dual_annihilator_dual_coannihilator_eq Subspace.dualAnnihilator_dualCoannihilator_eq
 -/
 
+#print Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff /-
 -- exact elaborates slowly
 theorem forall_mem_dualAnnihilator_apply_eq_zero_iff (W : Subspace K V) (v : V) :
     (∀ φ : Module.Dual K V, φ ∈ W.dualAnnihilator → φ v = 0) ↔ v ∈ W := by
   rw [← set_like.ext_iff.mp dual_annihilator_dual_coannihilator_eq v, mem_dual_coannihilator]
 #align subspace.forall_mem_dual_annihilator_apply_eq_zero_iff Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff
+-/
 
 #print Subspace.dualAnnihilatorGci /-
 /-- `submodule.dual_annihilator` and `submodule.dual_coannihilator` form a Galois coinsertion. -/
@@ -1077,14 +1211,18 @@ noncomputable def dualLift (W : Subspace K V) : Module.Dual K W →ₗ[K] Module
 
 variable {W : Subspace K V}
 
+#print Subspace.dualLift_of_subtype /-
 @[simp]
 theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w := by
   erw [of_is_compl_left_apply _ w]; rfl
 #align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtype
+-/
 
+#print Subspace.dualLift_of_mem /-
 theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLift φ w = φ ⟨w, hw⟩ :=
   by convert dual_lift_of_subtype ⟨w, hw⟩
 #align subspace.dual_lift_of_mem Subspace.dualLift_of_mem
+-/
 
 #print Subspace.dualRestrict_comp_dualLift /-
 @[simp]
@@ -1093,23 +1231,31 @@ theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.du
 #align subspace.dual_restrict_comp_dual_lift Subspace.dualRestrict_comp_dualLift
 -/
 
+#print Subspace.dualRestrict_leftInverse /-
 theorem dualRestrict_leftInverse (W : Subspace K V) :
     Function.LeftInverse W.dualRestrict W.dualLift := fun x =>
   show W.dualRestrict.comp W.dualLift x = x by rw [dual_restrict_comp_dual_lift]; rfl
 #align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverse
+-/
 
+#print Subspace.dualLift_rightInverse /-
 theorem dualLift_rightInverse (W : Subspace K V) :
     Function.RightInverse W.dualLift W.dualRestrict :=
   W.dualRestrict_leftInverse
 #align subspace.dual_lift_right_inverse Subspace.dualLift_rightInverse
+-/
 
+#print Subspace.dualRestrict_surjective /-
 theorem dualRestrict_surjective : Function.Surjective W.dualRestrict :=
   W.dualLift_rightInverse.Surjective
 #align subspace.dual_restrict_surjective Subspace.dualRestrict_surjective
+-/
 
+#print Subspace.dualLift_injective /-
 theorem dualLift_injective : Function.Injective W.dualLift :=
   W.dualRestrict_leftInverse.Injective
 #align subspace.dual_lift_injective Subspace.dualLift_injective
+-/
 
 #print Subspace.quotAnnihilatorEquiv /-
 /-- The quotient by the `dual_annihilator` of a subspace is isomorphic to the
@@ -1121,10 +1267,12 @@ noncomputable def quotAnnihilatorEquiv (W : Subspace K V) :
 #align subspace.quot_annihilator_equiv Subspace.quotAnnihilatorEquiv
 -/
 
+#print Subspace.quotAnnihilatorEquiv_apply /-
 @[simp]
 theorem quotAnnihilatorEquiv_apply (W : Subspace K V) (φ : Module.Dual K V) :
     W.quotAnnihilatorEquiv (Submodule.Quotient.mk φ) = W.dualRestrict φ := by ext; rfl
 #align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_apply
+-/
 
 #print Subspace.dualEquivDual /-
 /-- The natural isomorphism from the dual of a subspace `W` to `W.dual_lift.range`. -/
@@ -1140,11 +1288,13 @@ theorem dualEquivDual_def (W : Subspace K V) :
 #align subspace.dual_equiv_dual_def Subspace.dualEquivDual_def
 -/
 
+#print Subspace.dualEquivDual_apply /-
 @[simp]
 theorem dualEquivDual_apply (φ : Module.Dual K W) :
     W.dualEquivDual φ = ⟨W.dualLift φ, mem_range.2 ⟨φ, rfl⟩⟩ :=
   rfl
 #align subspace.dual_equiv_dual_apply Subspace.dualEquivDual_apply
+-/
 
 section
 
@@ -1158,6 +1308,7 @@ instance [H : FiniteDimensional K V] : FiniteDimensional K (Module.Dual K V) :=
 
 variable [FiniteDimensional K V] [FiniteDimensional K V₁]
 
+#print Subspace.dualAnnihilator_dualAnnihilator_eq /-
 theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
     W.dualAnnihilator.dualAnnihilator = Module.mapEvalEquiv K V W :=
   by
@@ -1165,6 +1316,7 @@ theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
   rw [dual_coannihilator, ← Module.mapEvalEquiv_symm_apply] at this 
   rwa [← OrderIso.symm_apply_eq]
 #align subspace.dual_annihilator_dual_annihilator_eq Subspace.dualAnnihilator_dualAnnihilator_eq
+-/
 
 #print Subspace.dual_finrank_eq /-
 -- TODO(kmill): https://github.com/leanprover-community/mathlib/pull/17521#discussion_r1083241963
@@ -1273,11 +1425,13 @@ def dualCopairing (W : Submodule R M) : W.dualAnnihilator →ₗ[R] M ⧸ W →
 #align submodule.dual_copairing Submodule.dualCopairing
 -/
 
+#print Submodule.dualCopairing_apply /-
 @[simp]
 theorem dualCopairing_apply {W : Submodule R M} (φ : W.dualAnnihilator) (x : M) :
     W.dualCopairing φ (Quotient.mk x) = φ x :=
   rfl
 #align submodule.dual_copairing_apply Submodule.dualCopairing_apply
+-/
 
 #print Submodule.dualPairing /-
 /-- Given a submodule, restrict to the pairing on `W` by
@@ -1291,12 +1445,15 @@ def dualPairing (W : Submodule R M) : Module.Dual R M ⧸ W.dualAnnihilator →
 #align submodule.dual_pairing Submodule.dualPairing
 -/
 
+#print Submodule.dualPairing_apply /-
 @[simp]
 theorem dualPairing_apply {W : Submodule R M} (φ : Module.Dual R M) (x : W) :
     W.dualPairing (Quotient.mk φ) x = φ x :=
   rfl
 #align submodule.dual_pairing_apply Submodule.dualPairing_apply
+-/
 
+#print Submodule.range_dualMap_mkQ_eq /-
 /-- That $\operatorname{im}(q^* : (V/W)^* \to V^*) = \operatorname{ann}(W)$. -/
 theorem range_dualMap_mkQ_eq (W : Submodule R M) : W.mkQ.dualMap.range = W.dualAnnihilator :=
   by
@@ -1311,6 +1468,7 @@ theorem range_dualMap_mkQ_eq (W : Submodule R M) : W.mkQ.dualMap.range = W.dualA
     ext
     rfl
 #align submodule.range_dual_map_mkq_eq Submodule.range_dualMap_mkQ_eq
+-/
 
 #print Submodule.dualQuotEquivDualAnnihilator /-
 /-- Equivalence $(M/W)^* \approx \operatorname{ann}(W)$. That is, there is a one-to-one
@@ -1327,22 +1485,28 @@ def dualQuotEquivDualAnnihilator (W : Submodule R M) :
 #align submodule.dual_quot_equiv_dual_annihilator Submodule.dualQuotEquivDualAnnihilator
 -/
 
+#print Submodule.dualQuotEquivDualAnnihilator_apply /-
 @[simp]
 theorem dualQuotEquivDualAnnihilator_apply (W : Submodule R M) (φ : Module.Dual R (M ⧸ W)) (x : M) :
     dualQuotEquivDualAnnihilator W φ x = φ (Quotient.mk x) :=
   rfl
 #align submodule.dual_quot_equiv_dual_annihilator_apply Submodule.dualQuotEquivDualAnnihilator_apply
+-/
 
+#print Submodule.dualCopairing_eq /-
 theorem dualCopairing_eq (W : Submodule R M) :
     W.dualCopairing = (dualQuotEquivDualAnnihilator W).symm.toLinearMap :=
   rfl
 #align submodule.dual_copairing_eq Submodule.dualCopairing_eq
+-/
 
+#print Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk /-
 @[simp]
 theorem dualQuotEquivDualAnnihilator_symm_apply_mk (W : Submodule R M) (φ : W.dualAnnihilator)
     (x : M) : (dualQuotEquivDualAnnihilator W).symm φ (Quotient.mk x) = φ x :=
   rfl
 #align submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk
+-/
 
 end Submodule
 
@@ -1350,6 +1514,7 @@ namespace LinearMap
 
 open Submodule
 
+#print LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective /-
 theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
     (hf : Function.Surjective f) : f.dualMap.range = f.ker.dualAnnihilator :=
   by
@@ -1365,7 +1530,9 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
       LinearEquiv.trans_symm, LinearEquiv.trans_apply, LinearEquiv.ofTop_symm_apply,
       LinearMap.quotKerEquivRange_symm_apply_image, mkq_apply]
 #align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective
+-/
 
+#print LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective /-
 -- Note, this can be specialized to the case where `R` is an injective `R`-module, or when
 -- `f.coker` is a projective `R`-module.
 theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M →ₗ[R] M')
@@ -1381,6 +1548,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M
   · apply congr_arg
     exact (LinearMap.ker_rangeRestrict f).symm
 #align linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective
+-/
 
 end LinearMap
 
@@ -1400,6 +1568,7 @@ theorem dualPairing_nondegenerate : (dualPairing K V₁).Nondegenerate :=
 #align linear_map.dual_pairing_nondegenerate LinearMap.dualPairing_nondegenerate
 -/
 
+#print LinearMap.dualMap_surjective_of_injective /-
 theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function.Injective f) :
     Function.Surjective f.dualMap := by
   intro φ
@@ -1411,6 +1580,7 @@ theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function
   congr 1
   exact LinearEquiv.symm_apply_apply f' x
 #align linear_map.dual_map_surjective_of_injective LinearMap.dualMap_surjective_of_injective
+-/
 
 #print LinearMap.range_dualMap_eq_dualAnnihilator_ker /-
 theorem range_dualMap_eq_dualAnnihilator_ker (f : V₁ →ₗ[K] V₂) :
@@ -1420,6 +1590,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker (f : V₁ →ₗ[K] V₂) :
 #align linear_map.range_dual_map_eq_dual_annihilator_ker LinearMap.range_dualMap_eq_dualAnnihilator_ker
 -/
 
+#print LinearMap.dualMap_surjective_iff /-
 /-- For vector spaces, `f.dual_map` is surjective if and only if `f` is injective -/
 @[simp]
 theorem dualMap_surjective_iff {f : V₁ →ₗ[K] V₂} :
@@ -1427,6 +1598,7 @@ theorem dualMap_surjective_iff {f : V₁ →ₗ[K] V₂} :
   rw [← LinearMap.range_eq_top, range_dual_map_eq_dual_annihilator_ker, ←
     Submodule.dualAnnihilator_bot, Subspace.dualAnnihilator_inj, LinearMap.ker_eq_bot]
 #align linear_map.dual_map_surjective_iff LinearMap.dualMap_surjective_iff
+-/
 
 end LinearMap
 
@@ -1488,6 +1660,7 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
 #align subspace.dual_annihilator_inf_eq Subspace.dualAnnihilator_inf_eq
 -/
 
+#print Subspace.dualAnnihilator_iInf_eq /-
 -- This is also true if `V₁` is finite dimensional since one can restrict `ι` to some subtype
 -- for which the infi and supr are the same.
 --
@@ -1507,6 +1680,7 @@ theorem dualAnnihilator_iInf_eq {ι : Type _} [Finite ι] (W : ι → Subspace K
   · intro α _ h W
     rw [iInf_option, iSup_option, dual_annihilator_inf_eq, h]
 #align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_iInf_eq
+-/
 
 #print Subspace.isCompl_dualAnnihilator /-
 /-- For vector spaces, dual annihilators carry direct sum decompositions
@@ -1557,6 +1731,7 @@ theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
 #align linear_map.finrank_range_dual_map_eq_finrank_range LinearMap.finrank_range_dualMap_eq_finrank_range
 -/
 
+#print LinearMap.dualMap_injective_iff /-
 /-- `f.dual_map` is injective if and only if `f` is surjective -/
 @[simp]
 theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
@@ -1571,13 +1746,16 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
     LinearMap.finrank_range_dualMap_eq_finrank_range, LinearMap.finrank_range_add_finrank_ker,
     Subspace.dual_finrank_eq]
 #align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iff
+-/
 
+#print LinearMap.dualMap_bijective_iff /-
 /-- `f.dual_map` is bijective if and only if `f` is -/
 @[simp]
 theorem dualMap_bijective_iff {f : V₁ →ₗ[K] V₂} :
     Function.Bijective f.dualMap ↔ Function.Bijective f := by
   simp_rw [Function.Bijective, dual_map_surjective_iff, dual_map_injective_iff, and_comm]
 #align linear_map.dual_map_bijective_iff LinearMap.dualMap_bijective_iff
+-/
 
 end LinearMap
 
@@ -1611,6 +1789,7 @@ variable [CommSemiring R] [AddCommMonoid M] [AddCommMonoid N]
 
 variable [Module R M] [Module R N]
 
+#print TensorProduct.dualDistrib /-
 /-- The canonical linear map from `dual M ⊗ dual N` to `dual (M ⊗ N)`,
 sending `f ⊗ g` to the composition of `tensor_product.map f g` with
 the natural isomorphism `R ⊗ R ≃ R`.
@@ -1618,14 +1797,17 @@ the natural isomorphism `R ⊗ R ≃ R`.
 def dualDistrib : Dual R M ⊗[R] Dual R N →ₗ[R] Dual R (M ⊗[R] N) :=
   compRight ↑(TensorProduct.lid R R) ∘ₗ homTensorHomMap R M N R R
 #align tensor_product.dual_distrib TensorProduct.dualDistrib
+-/
 
 variable {R M N}
 
+#print TensorProduct.dualDistrib_apply /-
 @[simp]
 theorem dualDistrib_apply (f : Dual R M) (g : Dual R N) (m : M) (n : N) :
     dualDistrib R M N (f ⊗ₜ g) (m ⊗ₜ n) = f m * g n :=
   rfl
 #align tensor_product.dual_distrib_apply TensorProduct.dualDistrib_apply
+-/
 
 end
 
@@ -1636,6 +1818,7 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N]
 variable [Module R M] [Module R N]
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print TensorProduct.dualDistribInvOfBasis /-
 /-- An inverse to `dual_tensor_dual_map` given bases.
 -/
 noncomputable def dualDistribInvOfBasis (b : Basis ι R M) (c : Basis κ R N) :
@@ -1644,14 +1827,18 @@ noncomputable def dualDistribInvOfBasis (b : Basis ι R M) (c : Basis κ R N) :
     (ringLmapEquivSelf R ℕ _).symm (b.dualBasis i ⊗ₜ c.dualBasis j) ∘ₗ
       applyₗ (c j) ∘ₗ applyₗ (b i) ∘ₗ lcurry R M N R
 #align tensor_product.dual_distrib_inv_of_basis TensorProduct.dualDistribInvOfBasis
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print TensorProduct.dualDistribInvOfBasis_apply /-
 @[simp]
 theorem dualDistribInvOfBasis_apply (b : Basis ι R M) (c : Basis κ R N) (f : Dual R (M ⊗[R] N)) :
     dualDistribInvOfBasis b c f = ∑ (i) (j), f (b i ⊗ₜ c j) • b.dualBasis i ⊗ₜ c.dualBasis j := by
   simp [dual_distrib_inv_of_basis]
 #align tensor_product.dual_distrib_inv_of_basis_apply TensorProduct.dualDistribInvOfBasis_apply
+-/
 
+#print TensorProduct.dualDistribEquivOfBasis /-
 /-- A linear equivalence between `dual M ⊗ dual N` and `dual (M ⊗ N)` given bases for `M` and `N`.
 It sends `f ⊗ g` to the composition of `tensor_product.map f g` with the natural
 isomorphism `R ⊗ R ≃ R`.
@@ -1672,6 +1859,7 @@ noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N)
       dual_distrib_apply, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis,
       Basis.sum_dual_apply_smul_coord]
 #align tensor_product.dual_distrib_equiv_of_basis TensorProduct.dualDistribEquivOfBasis
+-/
 
 variable (R M N)
 
@@ -1681,6 +1869,7 @@ variable [Nontrivial R]
 
 open scoped Classical
 
+#print TensorProduct.dualDistribEquiv /-
 /--
 A linear equivalence between `dual M ⊗ dual N` and `dual (M ⊗ N)` when `M` and `N` are finite free
 modules. It sends `f ⊗ g` to the composition of `tensor_product.map f g` with the natural
@@ -1690,6 +1879,7 @@ isomorphism `R ⊗ R ≃ R`.
 noncomputable def dualDistribEquiv : Dual R M ⊗[R] Dual R N ≃ₗ[R] Dual R (M ⊗[R] N) :=
   dualDistribEquivOfBasis (Module.Free.chooseBasis R M) (Module.Free.chooseBasis R N)
 #align tensor_product.dual_distrib_equiv TensorProduct.dualDistribEquiv
+-/
 
 end TensorProduct
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -395,7 +395,7 @@ variable (b : Basis ι R M)
 
 #print Basis.sum_dual_apply_smul_coord /-
 @[simp]
-theorem sum_dual_apply_smul_coord (f : Module.Dual R M) : (∑ x, f (b x) • b.Coord x) = f :=
+theorem sum_dual_apply_smul_coord (f : Module.Dual R M) : ∑ x, f (b x) • b.Coord x = f :=
   by
   ext m
   simp_rw [LinearMap.sum_apply, LinearMap.smul_apply, smul_eq_mul, mul_comm (f _), ← smul_eq_mul, ←

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -668,7 +668,7 @@ variable {R M ι : Type _}
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
 -- TODO: In Lean 4 we can remove this and use `by { intros; exact Set.toFinite _ }` as a default
 -- argument.
 /-- Try using `set.to_finite` to dispatch a `set.finite` goal. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

@@ -161,12 +161,10 @@ theorem transpose_apply (u : M →ₗ[R] M') (l : Dual R M') : transpose u l = l
 
 variable {M'' : Type _} [AddCommMonoid M''] [Module R M'']
 
-#print Module.Dual.transpose_comp /-
 theorem transpose_comp (u : M' →ₗ[R] M'') (v : M →ₗ[R] M') :
     transpose (u.comp v) = (transpose v).comp (transpose u) :=
   rfl
 #align module.dual.transpose_comp Module.Dual.transpose_comp
--/
 
 end Dual
 
@@ -206,11 +204,9 @@ def LinearMap.dualMap (f : M₁ →ₗ[R] M₂) : Dual R M₂ →ₗ[R] Dual R M
 #align linear_map.dual_map LinearMap.dualMap
 -/
 
-#print LinearMap.dualMap_def /-
 theorem LinearMap.dualMap_def (f : M₁ →ₗ[R] M₂) : f.dualMap = Module.Dual.transpose f :=
   rfl
 #align linear_map.dual_map_def LinearMap.dualMap_def
--/
 
 theorem LinearMap.dualMap_apply' (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) : f.dualMap g = g.comp f :=
   rfl
@@ -374,13 +370,10 @@ theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   rfl
 #align basis.to_dual_inj Basis.toDual_inj
 
-#print Basis.toDual_ker /-
 theorem toDual_ker : b.toDual.ker = ⊥ :=
   ker_eq_bot'.mpr b.toDual_inj
 #align basis.to_dual_ker Basis.toDual_ker
--/
 
-#print Basis.toDual_range /-
 theorem toDual_range [Finite ι] : b.toDual.range = ⊤ :=
   by
   cases nonempty_fintype ι
@@ -391,7 +384,6 @@ theorem toDual_range [Finite ι] : b.toDual.range = ⊤ :=
   rw [b.to_dual_eq_repr _ i, repr_total b]
   rfl
 #align basis.to_dual_range Basis.toDual_range
--/
 
 end CommSemiring
 
@@ -570,10 +562,8 @@ section
 
 variable (K) (V)
 
-#print Module.eval_ker /-
 theorem eval_ker : (eval K V).ker = ⊥ := by classical exact (Basis.ofVectorSpace K V).eval_ker
 #align module.eval_ker Module.eval_ker
--/
 
 #print Module.map_eval_injective /-
 theorem map_eval_injective : (Submodule.map (eval K V)).Injective :=
@@ -601,17 +591,13 @@ section
 
 variable (K)
 
-#print Module.eval_apply_eq_zero_iff /-
 theorem eval_apply_eq_zero_iff (v : V) : (eval K V) v = 0 ↔ v = 0 := by
   simpa only using set_like.ext_iff.mp (eval_ker K V) v
 #align module.eval_apply_eq_zero_iff Module.eval_apply_eq_zero_iff
--/
 
-#print Module.eval_apply_injective /-
 theorem eval_apply_injective : Function.Injective (eval K V) :=
   (injective_iff_map_eq_zero' (eval K V)).mpr (eval_apply_eq_zero_iff K)
 #align module.eval_apply_injective Module.eval_apply_injective
--/
 
 theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v = 0) ↔ v = 0 := by
   rw [← eval_apply_eq_zero_iff K v, LinearMap.ext_iff]; rfl
@@ -627,12 +613,10 @@ theorem dual_rank_eq [FiniteDimensional K V] :
 #align module.dual_rank_eq Module.dual_rank_eq
 -/
 
-#print Module.erange_coe /-
 theorem erange_coe [FiniteDimensional K V] : (eval K V).range = ⊤ :=
   letI : IsNoetherian K V := IsNoetherian.iff_fg.2 inferInstance
   (Basis.ofVectorSpace K V).eval_range
 #align module.erange_coe Module.erange_coe
--/
 
 variable (K V)
 
@@ -662,21 +646,17 @@ theorem evalEquiv_toLinearMap [FiniteDimensional K V] :
 #align module.eval_equiv_to_linear_map Module.evalEquiv_toLinearMap
 -/
 
-#print Module.mapEvalEquiv_apply /-
 @[simp]
 theorem mapEvalEquiv_apply [FiniteDimensional K V] (W : Subspace K V) :
     mapEvalEquiv K V W = W.map (eval K V) :=
   rfl
 #align module.map_eval_equiv_apply Module.mapEvalEquiv_apply
--/
 
-#print Module.mapEvalEquiv_symm_apply /-
 @[simp]
 theorem mapEvalEquiv_symm_apply [FiniteDimensional K V] (W'' : Subspace K (Dual K (Dual K V))) :
     (mapEvalEquiv K V).symm W'' = W''.comap (eval K V) :=
   rfl
 #align module.map_eval_equiv_symm_apply Module.mapEvalEquiv_symm_apply
--/
 
 end Module
 
@@ -877,12 +857,10 @@ def dualCoannihilator (Φ : Submodule R (Module.Dual R M)) : Submodule R M :=
 #align submodule.dual_coannihilator Submodule.dualCoannihilator
 -/
 
-#print Submodule.mem_dualCoannihilator /-
 theorem mem_dualCoannihilator {Φ : Submodule R (Module.Dual R M)} (x : M) :
     x ∈ Φ.dualCoannihilator ↔ ∀ φ ∈ Φ, (φ x : R) = 0 := by
   simp_rw [dual_coannihilator, mem_comap, mem_dual_annihilator, Module.Dual.eval_apply]
 #align submodule.mem_dual_coannihilator Submodule.mem_dualCoannihilator
--/
 
 theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Module R M] :
     GaloisConnection
@@ -908,14 +886,11 @@ theorem le_dualAnnihilator_iff_le_dualCoannihilator {U : Submodule R (Module.Dua
 #align submodule.le_dual_annihilator_iff_le_dual_coannihilator Submodule.le_dualAnnihilator_iff_le_dualCoannihilator
 -/
 
-#print Submodule.dualAnnihilator_bot /-
 @[simp]
 theorem dualAnnihilator_bot : (⊥ : Submodule R M).dualAnnihilator = ⊤ :=
   (dualAnnihilator_gc R M).l_bot
 #align submodule.dual_annihilator_bot Submodule.dualAnnihilator_bot
--/
 
-#print Submodule.dualAnnihilator_top /-
 @[simp]
 theorem dualAnnihilator_top : (⊤ : Submodule R M).dualAnnihilator = ⊥ :=
   by
@@ -924,14 +899,11 @@ theorem dualAnnihilator_top : (⊤ : Submodule R M).dualAnnihilator = ⊥ :=
   simp_rw [mem_dual_annihilator, mem_bot, mem_top, forall_true_left]
   exact fun h => LinearMap.ext h
 #align submodule.dual_annihilator_top Submodule.dualAnnihilator_top
--/
 
-#print Submodule.dualCoannihilator_bot /-
 @[simp]
 theorem dualCoannihilator_bot : (⊥ : Submodule R (Module.Dual R M)).dualCoannihilator = ⊤ :=
   (dualAnnihilator_gc R M).u_top
 #align submodule.dual_coannihilator_bot Submodule.dualCoannihilator_bot
--/
 
 #print Submodule.dualAnnihilator_anti /-
 @[mono]
@@ -977,19 +949,15 @@ theorem dualCoannihilator_dualAnnihilator_dualCoannihilator (U : Submodule R (Mo
 #align submodule.dual_coannihilator_dual_annihilator_dual_coannihilator Submodule.dualCoannihilator_dualAnnihilator_dualCoannihilator
 -/
 
-#print Submodule.dualAnnihilator_sup_eq /-
 theorem dualAnnihilator_sup_eq (U V : Submodule R M) :
     (U ⊔ V).dualAnnihilator = U.dualAnnihilator ⊓ V.dualAnnihilator :=
   (dualAnnihilator_gc R M).l_sup
 #align submodule.dual_annihilator_sup_eq Submodule.dualAnnihilator_sup_eq
--/
 
-#print Submodule.dualCoannihilator_sup_eq /-
 theorem dualCoannihilator_sup_eq (U V : Submodule R (Module.Dual R M)) :
     (U ⊔ V).dualCoannihilator = U.dualCoannihilator ⊓ V.dualCoannihilator :=
   (dualAnnihilator_gc R M).u_inf
 #align submodule.dual_coannihilator_sup_eq Submodule.dualCoannihilator_sup_eq
--/
 
 theorem dualAnnihilator_iSup_eq {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, U i).dualAnnihilator = ⨅ i : ι, (U i).dualAnnihilator :=
@@ -1001,7 +969,6 @@ theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.
   (dualAnnihilator_gc R M).u_iInf
 #align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
 
-#print Submodule.sup_dualAnnihilator_le_inf /-
 /-- See also `subspace.dual_annihilator_inf_eq` for vector subspaces. -/
 theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
     U.dualAnnihilator ⊔ V.dualAnnihilator ≤ (U ⊓ V).dualAnnihilator :=
@@ -1009,7 +976,6 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
   rw [le_dual_annihilator_iff_le_dual_coannihilator, dual_coannihilator_sup_eq]
   apply inf_le_inf <;> exact le_dual_annihilator_dual_coannihilator _
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
--/
 
 /-- See also `subspace.dual_annihilator_infi_eq` for vector subspaces when `ι` is finite. -/
 theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
@@ -1031,13 +997,11 @@ universe u v w
 -- We work in vector spaces because `exists_is_compl` only hold for vector spaces
 variable {K : Type u} {V : Type v} [Field K] [AddCommGroup V] [Module K V]
 
-#print Subspace.dualCoannihilator_top /-
 @[simp]
 theorem dualCoannihilator_top (W : Subspace K V) :
     (⊤ : Subspace K (Module.Dual K W)).dualCoannihilator = ⊥ := by
   rw [dual_coannihilator, dual_annihilator_top, comap_bot, Module.eval_ker]
 #align subspace.dual_coannihilator_top Subspace.dualCoannihilator_top
--/
 
 #print Subspace.dualAnnihilator_dualCoannihilator_eq /-
 theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
@@ -1194,7 +1158,6 @@ instance [H : FiniteDimensional K V] : FiniteDimensional K (Module.Dual K V) :=
 
 variable [FiniteDimensional K V] [FiniteDimensional K V₁]
 
-#print Subspace.dualAnnihilator_dualAnnihilator_eq /-
 theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
     W.dualAnnihilator.dualAnnihilator = Module.mapEvalEquiv K V W :=
   by
@@ -1202,7 +1165,6 @@ theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
   rw [dual_coannihilator, ← Module.mapEvalEquiv_symm_apply] at this 
   rwa [← OrderIso.symm_apply_eq]
 #align subspace.dual_annihilator_dual_annihilator_eq Subspace.dualAnnihilator_dualAnnihilator_eq
--/
 
 #print Subspace.dual_finrank_eq /-
 -- TODO(kmill): https://github.com/leanprover-community/mathlib/pull/17521#discussion_r1083241963
@@ -1649,7 +1611,6 @@ variable [CommSemiring R] [AddCommMonoid M] [AddCommMonoid N]
 
 variable [Module R M] [Module R N]
 
-#print TensorProduct.dualDistrib /-
 /-- The canonical linear map from `dual M ⊗ dual N` to `dual (M ⊗ N)`,
 sending `f ⊗ g` to the composition of `tensor_product.map f g` with
 the natural isomorphism `R ⊗ R ≃ R`.
@@ -1657,7 +1618,6 @@ the natural isomorphism `R ⊗ R ≃ R`.
 def dualDistrib : Dual R M ⊗[R] Dual R N →ₗ[R] Dual R (M ⊗[R] N) :=
   compRight ↑(TensorProduct.lid R R) ∘ₗ homTensorHomMap R M N R R
 #align tensor_product.dual_distrib TensorProduct.dualDistrib
--/
 
 variable {R M N}
 
@@ -1692,7 +1652,6 @@ theorem dualDistribInvOfBasis_apply (b : Basis ι R M) (c : Basis κ R N) (f : D
   simp [dual_distrib_inv_of_basis]
 #align tensor_product.dual_distrib_inv_of_basis_apply TensorProduct.dualDistribInvOfBasis_apply
 
-#print TensorProduct.dualDistribEquivOfBasis /-
 /-- A linear equivalence between `dual M ⊗ dual N` and `dual (M ⊗ N)` given bases for `M` and `N`.
 It sends `f ⊗ g` to the composition of `tensor_product.map f g` with the natural
 isomorphism `R ⊗ R ≃ R`.
@@ -1713,7 +1672,6 @@ noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N)
       dual_distrib_apply, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis,
       Basis.sum_dual_apply_smul_coord]
 #align tensor_product.dual_distrib_equiv_of_basis TensorProduct.dualDistribEquivOfBasis
--/
 
 variable (R M N)
 
@@ -1723,7 +1681,6 @@ variable [Nontrivial R]
 
 open scoped Classical
 
-#print TensorProduct.dualDistribEquiv /-
 /--
 A linear equivalence between `dual M ⊗ dual N` and `dual (M ⊗ N)` when `M` and `N` are finite free
 modules. It sends `f ⊗ g` to the composition of `tensor_product.map f g` with the natural
@@ -1733,7 +1690,6 @@ isomorphism `R ⊗ R ≃ R`.
 noncomputable def dualDistribEquiv : Dual R M ⊗[R] Dual R N ≃ₗ[R] Dual R (M ⊗[R] N) :=
   dualDistribEquivOfBasis (Module.Free.chooseBasis R M) (Module.Free.chooseBasis R N)
 #align tensor_product.dual_distrib_equiv TensorProduct.dualDistribEquiv
--/
 
 end TensorProduct
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -499,9 +499,9 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
 
 theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by
   classical
-    cases nonempty_fintype ι
-    rw [← b.to_dual_to_dual, range_comp, b.to_dual_range, Submodule.map_top, to_dual_range _]
-    infer_instance
+  cases nonempty_fintype ι
+  rw [← b.to_dual_to_dual, range_comp, b.to_dual_range, Submodule.map_top, to_dual_range _]
+  infer_instance
 #align basis.eval_range Basis.eval_range
 
 #print Basis.evalEquiv /-
@@ -549,11 +549,11 @@ theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b :
 theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
     Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by
   classical
-    cases nonempty_fintype ι
-    have := LinearEquiv.lift_rank_eq b.to_dual_equiv
-    simp only [Cardinal.lift_umax] at this 
-    rw [this, ← Cardinal.lift_umax]
-    apply Cardinal.lift_id
+  cases nonempty_fintype ι
+  have := LinearEquiv.lift_rank_eq b.to_dual_equiv
+  simp only [Cardinal.lift_umax] at this 
+  rw [this, ← Cardinal.lift_umax]
+  apply Cardinal.lift_id
 #align basis.dual_rank_eq Basis.dual_rank_eq
 
 end Basis
@@ -703,7 +703,7 @@ unsafe def use_finite_instance : tactic Unit :=
 structure Module.DualBases (e : ι → M) (ε : ι → Dual R M) : Prop where
   eval : ∀ i j : ι, ε i (e j) = if i = j then 1 else 0
   Total : ∀ {m : M}, (∀ i, ε i m = 0) → m = 0
-  Finite : ∀ m : M, { i | ε i m ≠ 0 }.Finite := by
+  Finite : ∀ m : M, {i | ε i m ≠ 0}.Finite := by
     run_tac
       use_finite_instance
 #align module.dual_bases Module.DualBases
@@ -1053,7 +1053,7 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
   have hw'n : (w' : V) ∉ W := by contrapose! hv; exact Submodule.add_mem W w.2 hv
   have hw'nz : w' ≠ 0 := by rintro rfl; exact hw'n (Submodule.zero_mem W)
   rw [Ne.def, ← Module.forall_dual_apply_eq_zero_iff K w'] at hw'nz 
-  push_neg  at hw'nz 
+  push_neg at hw'nz 
   obtain ⟨φ, hφ⟩ := hw'nz
   exists ((LinearMap.ofIsComplProd hW).comp (LinearMap.inr _ _ _)) φ
   simp only [coe_comp, coe_inr, Function.comp_apply, of_is_compl_prod_apply, map_add,

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -456,7 +456,7 @@ theorem total_dualBasis (f : ι →₀ R) (i : ι) :
   ·
     simp_rw [LinearMap.smul_apply, smul_eq_mul, dual_basis_apply_self, mul_boole, Finset.sum_ite_eq,
       if_pos (Finset.mem_univ i)]
-  · intro ; rw [zero_smul]
+  · intro; rw [zero_smul]
 #align basis.total_dual_basis Basis.total_dualBasis
 
 theorem dualBasis_repr (l : Dual R M) (i : ι) : b.dualBasis.repr l i = l (b i) := by
@@ -493,7 +493,7 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   by
   rw [ker_eq_bot']
   intro m hm
-  simp_rw [LinearMap.ext_iff, dual.eval_apply, zero_apply] at hm
+  simp_rw [LinearMap.ext_iff, dual.eval_apply, zero_apply] at hm 
   exact (Basis.forall_coord_eq_zero_iff _).mp fun i => hm (b.coord i)
 #align basis.eval_ker Basis.eval_ker
 
@@ -551,7 +551,7 @@ theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b :
   classical
     cases nonempty_fintype ι
     have := LinearEquiv.lift_rank_eq b.to_dual_equiv
-    simp only [Cardinal.lift_umax] at this
+    simp only [Cardinal.lift_umax] at this 
     rw [this, ← Cardinal.lift_umax]
     apply Cardinal.lift_id
 #align basis.dual_rank_eq Basis.dual_rank_eq
@@ -803,7 +803,7 @@ theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '
   intro i hi
   rcases(Finsupp.mem_span_image_iff_total _).mp hmem with ⟨l, supp_l, rfl⟩
   apply not_imp_comm.mp ((Finsupp.mem_supported' _ _).mp supp_l i)
-  rwa [← lc_def, h.dual_lc] at hi
+  rwa [← lc_def, h.dual_lc] at hi 
 #align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_span
 
 theorem coe_dualBasis [Fintype ι] : ⇑h.Basis.dualBasis = ε :=
@@ -897,7 +897,7 @@ theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Mo
       simp only [mem_dual_annihilator, mem_dual_coannihilator]
       intro y hy
       have := h hy
-      simp only [mem_dual_annihilator, mem_dual_coannihilator] at this
+      simp only [mem_dual_annihilator, mem_dual_coannihilator] at this 
       exact this x hx
 #align submodule.dual_annihilator_gc Submodule.dualAnnihilator_gc
 
@@ -1052,8 +1052,8 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
   obtain ⟨⟨w, w'⟩, rfl, -⟩ := exists_unique_add_of_is_compl_prod hW v
   have hw'n : (w' : V) ∉ W := by contrapose! hv; exact Submodule.add_mem W w.2 hv
   have hw'nz : w' ≠ 0 := by rintro rfl; exact hw'n (Submodule.zero_mem W)
-  rw [Ne.def, ← Module.forall_dual_apply_eq_zero_iff K w'] at hw'nz
-  push_neg  at hw'nz
+  rw [Ne.def, ← Module.forall_dual_apply_eq_zero_iff K w'] at hw'nz 
+  push_neg  at hw'nz 
   obtain ⟨φ, hφ⟩ := hw'nz
   exists ((LinearMap.ofIsComplProd hW).comp (LinearMap.inr _ _ _)) φ
   simp only [coe_comp, coe_inr, Function.comp_apply, of_is_compl_prod_apply, map_add,
@@ -1199,7 +1199,7 @@ theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
     W.dualAnnihilator.dualAnnihilator = Module.mapEvalEquiv K V W :=
   by
   have : _ = W := Subspace.dualAnnihilator_dualCoannihilator_eq
-  rw [dual_coannihilator, ← Module.mapEvalEquiv_symm_apply] at this
+  rw [dual_coannihilator, ← Module.mapEvalEquiv_symm_apply] at this 
   rwa [← OrderIso.symm_apply_eq]
 #align subspace.dual_annihilator_dual_annihilator_eq Subspace.dualAnnihilator_dualAnnihilator_eq
 -/
@@ -1268,13 +1268,13 @@ variable (f : M₁ →ₗ[R] M₂)
 theorem ker_dualMap_eq_dualAnnihilator_range : f.dualMap.ker = f.range.dualAnnihilator :=
   by
   ext φ; constructor <;> intro hφ
-  · rw [mem_ker] at hφ
+  · rw [mem_ker] at hφ 
     rw [Submodule.mem_dualAnnihilator]
     rintro y ⟨x, rfl⟩
     rw [← dual_map_apply, hφ, zero_apply]
   · ext x
     rw [dual_map_apply]
-    rw [Submodule.mem_dualAnnihilator] at hφ
+    rw [Submodule.mem_dualAnnihilator] at hφ 
     exact hφ (f x) ⟨x, rfl⟩
 #align linear_map.ker_dual_map_eq_dual_annihilator_range LinearMap.ker_dualMap_eq_dualAnnihilator_range
 -/
@@ -1552,7 +1552,7 @@ to direct sum decompositions. -/
 theorem isCompl_dualAnnihilator {W W' : Subspace K V₁} (h : IsCompl W W') :
     IsCompl W.dualAnnihilator W'.dualAnnihilator :=
   by
-  rw [isCompl_iff, disjoint_iff, codisjoint_iff] at h⊢
+  rw [isCompl_iff, disjoint_iff, codisjoint_iff] at h ⊢
   rw [← dual_annihilator_inf_eq, ← dual_annihilator_sup_eq, h.1, h.2, dual_annihilator_top,
     dual_annihilator_bot]
   exact ⟨rfl, rfl⟩
@@ -1587,7 +1587,7 @@ theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
   by
   have := Submodule.finrank_quotient_add_finrank f.range
   rw [(Subspace.quotEquivAnnihilator f.range).finrank_eq, ←
-    ker_dual_map_eq_dual_annihilator_range] at this
+    ker_dual_map_eq_dual_annihilator_range] at this 
   conv_rhs at this => rw [← Subspace.dual_finrank_eq]
   refine' add_left_injective (finrank K f.dual_map.ker) _
   change _ + _ = _ + _
@@ -1604,7 +1604,7 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
   rw [← range_eq_top, ← ker_eq_bot]
   intro h
   apply FiniteDimensional.eq_top_of_finrank_eq
-  rw [← finrank_eq_zero] at h
+  rw [← finrank_eq_zero] at h 
   rw [← add_zero (FiniteDimensional.finrank K f.range), ← h, ←
     LinearMap.finrank_range_dualMap_eq_finrank_range, LinearMap.finrank_range_add_finrank_ker,
     Subspace.dual_finrank_eq]

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -292,7 +292,7 @@ universe u v w
 
 open Module Module.Dual Submodule LinearMap Cardinal Function
 
-open BigOperators
+open scoped BigOperators
 
 variable {R M K V ι : Type _}
 
@@ -519,7 +519,7 @@ theorem evalEquiv_toLinearMap {ι : Type _} [Finite ι] (b : Basis ι R M) :
 
 section
 
-open Classical
+open scoped Classical
 
 variable [Finite R M] [Free R M] [Nontrivial R]
 
@@ -933,11 +933,13 @@ theorem dualCoannihilator_bot : (⊥ : Submodule R (Module.Dual R M)).dualCoanni
 #align submodule.dual_coannihilator_bot Submodule.dualCoannihilator_bot
 -/
 
+#print Submodule.dualAnnihilator_anti /-
 @[mono]
 theorem dualAnnihilator_anti {U V : Submodule R M} (hUV : U ≤ V) :
     V.dualAnnihilator ≤ U.dualAnnihilator :=
   (dualAnnihilator_gc R M).monotone_l hUV
 #align submodule.dual_annihilator_anti Submodule.dualAnnihilator_anti
+-/
 
 #print Submodule.dualCoannihilator_anti /-
 @[mono]
@@ -947,10 +949,12 @@ theorem dualCoannihilator_anti {U V : Submodule R (Module.Dual R M)} (hUV : U 
 #align submodule.dual_coannihilator_anti Submodule.dualCoannihilator_anti
 -/
 
+#print Submodule.le_dualAnnihilator_dualCoannihilator /-
 theorem le_dualAnnihilator_dualCoannihilator (U : Submodule R M) :
     U ≤ U.dualAnnihilator.dualCoannihilator :=
   (dualAnnihilator_gc R M).le_u_l U
 #align submodule.le_dual_annihilator_dual_coannihilator Submodule.le_dualAnnihilator_dualCoannihilator
+-/
 
 #print Submodule.le_dualCoannihilator_dualAnnihilator /-
 theorem le_dualCoannihilator_dualAnnihilator (U : Submodule R (Module.Dual R M)) :
@@ -997,6 +1001,7 @@ theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.
   (dualAnnihilator_gc R M).u_iInf
 #align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
 
+#print Submodule.sup_dualAnnihilator_le_inf /-
 /-- See also `subspace.dual_annihilator_inf_eq` for vector subspaces. -/
 theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
     U.dualAnnihilator ⊔ V.dualAnnihilator ≤ (U ⊓ V).dualAnnihilator :=
@@ -1004,6 +1009,7 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
   rw [le_dual_annihilator_iff_le_dual_coannihilator, dual_coannihilator_sup_eq]
   apply inf_le_inf <;> exact le_dual_annihilator_dual_coannihilator _
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
+-/
 
 /-- See also `subspace.dual_annihilator_infi_eq` for vector subspaces when `ι` is finite. -/
 theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
@@ -1078,10 +1084,12 @@ def dualAnnihilatorGci (K V : Type _) [Field K] [AddCommGroup V] [Module K V] :
 #align subspace.dual_annihilator_gci Subspace.dualAnnihilatorGci
 -/
 
+#print Subspace.dualAnnihilator_le_dualAnnihilator_iff /-
 theorem dualAnnihilator_le_dualAnnihilator_iff {W W' : Subspace K V} :
     W.dualAnnihilator ≤ W'.dualAnnihilator ↔ W' ≤ W :=
   (dualAnnihilatorGci K V).l_le_l_iff
 #align subspace.dual_annihilator_le_dual_annihilator_iff Subspace.dualAnnihilator_le_dualAnnihilator_iff
+-/
 
 #print Subspace.dualAnnihilator_inj /-
 theorem dualAnnihilator_inj {W W' : Subspace K V} :
@@ -1176,7 +1184,7 @@ theorem dualEquivDual_apply (φ : Module.Dual K W) :
 
 section
 
-open Classical
+open scoped Classical
 
 open FiniteDimensional
 
@@ -1271,6 +1279,7 @@ theorem ker_dualMap_eq_dualAnnihilator_range : f.dualMap.ker = f.range.dualAnnih
 #align linear_map.ker_dual_map_eq_dual_annihilator_range LinearMap.ker_dualMap_eq_dualAnnihilator_range
 -/
 
+#print LinearMap.range_dualMap_le_dualAnnihilator_ker /-
 theorem range_dualMap_le_dualAnnihilator_ker : f.dualMap.range ≤ f.ker.dualAnnihilator :=
   by
   rintro _ ⟨ψ, rfl⟩
@@ -1278,6 +1287,7 @@ theorem range_dualMap_le_dualAnnihilator_ker : f.dualMap.range ≤ f.ker.dualAnn
   rintro x hx
   rw [dual_map_apply, hx, map_zero]
 #align linear_map.range_dual_map_le_dual_annihilator_ker LinearMap.range_dualMap_le_dualAnnihilator_ker
+-/
 
 end LinearMap
 
@@ -1623,9 +1633,9 @@ variable [DecidableEq ι] [DecidableEq κ]
 
 variable [Fintype ι] [Fintype κ]
 
-open BigOperators
+open scoped BigOperators
 
-open TensorProduct
+open scoped TensorProduct
 
 attribute [local ext] TensorProduct.ext
 
@@ -1711,7 +1721,7 @@ variable [Module.Finite R M] [Module.Finite R N] [Module.Free R M] [Module.Free
 
 variable [Nontrivial R]
 
-open Classical
+open scoped Classical
 
 #print TensorProduct.dualDistribEquiv /-
 /--

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -119,9 +119,6 @@ def dualPairing (R M) [CommSemiring R] [AddCommMonoid M] [Module R M] :
 #align module.dual_pairing Module.dualPairing
 -/
 
-/- warning: module.dual_pairing_apply -> Module.dualPairing_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.dual_pairing_apply Module.dualPairing_applyₓ'. -/
 @[simp]
 theorem dualPairing_apply (v x) : dualPairing R M v x = v x :=
   rfl
@@ -143,9 +140,6 @@ def eval : M →ₗ[R] Dual R (Dual R M) :=
 #align module.dual.eval Module.Dual.eval
 -/
 
-/- warning: module.dual.eval_apply -> Module.Dual.eval_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.dual.eval_apply Module.Dual.eval_applyₓ'. -/
 @[simp]
 theorem eval_apply (v : M) (a : Dual R M) : eval R M v a = a v :=
   rfl
@@ -161,9 +155,6 @@ def transpose : (M →ₗ[R] M') →ₗ[R] Dual R M' →ₗ[R] Dual R M :=
 #align module.dual.transpose Module.Dual.transpose
 -/
 
-/- warning: module.dual.transpose_apply -> Module.Dual.transpose_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.dual.transpose_apply Module.Dual.transpose_applyₓ'. -/
 theorem transpose_apply (u : M →ₗ[R] M') (l : Dual R M') : transpose u l = l.comp u :=
   rfl
 #align module.dual.transpose_apply Module.Dual.transpose_apply
@@ -183,18 +174,12 @@ section Prod
 
 variable (M' : Type _) [AddCommMonoid M'] [Module R M']
 
-/- warning: module.dual_prod_dual_equiv_dual -> Module.dualProdDualEquivDual is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.dual_prod_dual_equiv_dual Module.dualProdDualEquivDualₓ'. -/
 /-- Taking duals distributes over products. -/
 @[simps]
 def dualProdDualEquivDual : (Module.Dual R M × Module.Dual R M') ≃ₗ[R] Module.Dual R (M × M') :=
   LinearMap.coprodEquiv R
 #align module.dual_prod_dual_equiv_dual Module.dualProdDualEquivDual
 
-/- warning: module.dual_prod_dual_equiv_dual_apply -> Module.dualProdDualEquivDual_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.dual_prod_dual_equiv_dual_apply Module.dualProdDualEquivDual_applyₓ'. -/
 @[simp]
 theorem dualProdDualEquivDual_apply (φ : Module.Dual R M) (ψ : Module.Dual R M') :
     dualProdDualEquivDual R M M' (φ, ψ) = φ.coprod ψ :=
@@ -227,16 +212,10 @@ theorem LinearMap.dualMap_def (f : M₁ →ₗ[R] M₂) : f.dualMap = Module.Dua
 #align linear_map.dual_map_def LinearMap.dualMap_def
 -/
 
-/- warning: linear_map.dual_map_apply' -> LinearMap.dualMap_apply' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_apply' LinearMap.dualMap_apply'ₓ'. -/
 theorem LinearMap.dualMap_apply' (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) : f.dualMap g = g.comp f :=
   rfl
 #align linear_map.dual_map_apply' LinearMap.dualMap_apply'
 
-/- warning: linear_map.dual_map_apply -> LinearMap.dualMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_apply LinearMap.dualMap_applyₓ'. -/
 @[simp]
 theorem LinearMap.dualMap_apply (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
     f.dualMap g x = g (f x) :=
@@ -249,17 +228,11 @@ theorem LinearMap.dualMap_id : (LinearMap.id : M₁ →ₗ[R] M₁).dualMap = Li
 #align linear_map.dual_map_id LinearMap.dualMap_id
 -/
 
-/- warning: linear_map.dual_map_comp_dual_map -> LinearMap.dualMap_comp_dualMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_comp_dual_map LinearMap.dualMap_comp_dualMapₓ'. -/
 theorem LinearMap.dualMap_comp_dualMap {M₃ : Type _} [AddCommGroup M₃] [Module R M₃]
     (f : M₁ →ₗ[R] M₂) (g : M₂ →ₗ[R] M₃) : f.dualMap.comp g.dualMap = (g.comp f).dualMap :=
   rfl
 #align linear_map.dual_map_comp_dual_map LinearMap.dualMap_comp_dualMap
 
-/- warning: linear_map.dual_map_injective_of_surjective -> LinearMap.dualMap_injective_of_surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_injective_of_surjective LinearMap.dualMap_injective_of_surjectiveₓ'. -/
 /-- If a linear map is surjective, then its dual is injective. -/
 theorem LinearMap.dualMap_injective_of_surjective {f : M₁ →ₗ[R] M₂} (hf : Function.Surjective f) :
     Function.Injective f.dualMap := by
@@ -285,9 +258,6 @@ def LinearEquiv.dualMap (f : M₁ ≃ₗ[R] M₂) : Dual R M₂ ≃ₗ[R] Dual R
 #align linear_equiv.dual_map LinearEquiv.dualMap
 -/
 
-/- warning: linear_equiv.dual_map_apply -> LinearEquiv.dualMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_equiv.dual_map_apply LinearEquiv.dualMap_applyₓ'. -/
 @[simp]
 theorem LinearEquiv.dualMap_apply (f : M₁ ≃ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
     f.dualMap g x = g (f x) :=
@@ -309,9 +279,6 @@ theorem LinearEquiv.dualMap_symm {f : M₁ ≃ₗ[R] M₂} :
 #align linear_equiv.dual_map_symm LinearEquiv.dualMap_symm
 -/
 
-/- warning: linear_equiv.dual_map_trans -> LinearEquiv.dualMap_trans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_equiv.dual_map_trans LinearEquiv.dualMap_transₓ'. -/
 theorem LinearEquiv.dualMap_trans {M₃ : Type _} [AddCommGroup M₃] [Module R M₃] (f : M₁ ≃ₗ[R] M₂)
     (g : M₂ ≃ₗ[R] M₃) : g.dualMap.trans f.dualMap = (f.trans g).dualMap :=
   rfl
@@ -343,16 +310,10 @@ def toDual : M →ₗ[R] Module.Dual R M :=
 #align basis.to_dual Basis.toDual
 -/
 
-/- warning: basis.to_dual_apply -> Basis.toDual_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply Basis.toDual_applyₓ'. -/
 theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0 := by
   erw [constr_basis b, constr_basis b]; ac_rfl
 #align basis.to_dual_apply Basis.toDual_apply
 
-/- warning: basis.to_dual_total_left -> Basis.toDual_total_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_total_left Basis.toDual_total_leftₓ'. -/
 @[simp]
 theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total ι M R b f) (b i) = f i :=
   by
@@ -364,9 +325,6 @@ theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total 
   · rw [finsupp.not_mem_support_iff.mp h]
 #align basis.to_dual_total_left Basis.toDual_total_left
 
-/- warning: basis.to_dual_total_right -> Basis.toDual_total_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_total_right Basis.toDual_total_rightₓ'. -/
 @[simp]
 theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.total ι M R b f) = f i :=
   by
@@ -377,23 +335,14 @@ theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.
   · rw [finsupp.not_mem_support_iff.mp h]
 #align basis.to_dual_total_right Basis.toDual_total_right
 
-/- warning: basis.to_dual_apply_left -> Basis.toDual_apply_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply_left Basis.toDual_apply_leftₓ'. -/
 theorem toDual_apply_left (m : M) (i : ι) : b.toDual m (b i) = b.repr m i := by
   rw [← b.to_dual_total_left, b.total_repr]
 #align basis.to_dual_apply_left Basis.toDual_apply_left
 
-/- warning: basis.to_dual_apply_right -> Basis.toDual_apply_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply_right Basis.toDual_apply_rightₓ'. -/
 theorem toDual_apply_right (i : ι) (m : M) : b.toDual (b i) m = b.repr m i := by
   rw [← b.to_dual_total_right, b.total_repr]
 #align basis.to_dual_apply_right Basis.toDual_apply_right
 
-/- warning: basis.coe_to_dual_self -> Basis.coe_toDual_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.coe_to_dual_self Basis.coe_toDual_selfₓ'. -/
 theorem coe_toDual_self (i : ι) : b.toDual (b i) = b.Coord i := by ext; apply to_dual_apply_right
 #align basis.coe_to_dual_self Basis.coe_toDual_self
 
@@ -404,30 +353,18 @@ def toDualFlip (m : M) : M →ₗ[R] R :=
 #align basis.to_dual_flip Basis.toDualFlip
 -/
 
-/- warning: basis.to_dual_flip_apply -> Basis.toDualFlip_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_flip_apply Basis.toDualFlip_applyₓ'. -/
 theorem toDualFlip_apply (m₁ m₂ : M) : b.toDualFlip m₁ m₂ = b.toDual m₂ m₁ :=
   rfl
 #align basis.to_dual_flip_apply Basis.toDualFlip_apply
 
-/- warning: basis.to_dual_eq_repr -> Basis.toDual_eq_repr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_eq_repr Basis.toDual_eq_reprₓ'. -/
 theorem toDual_eq_repr (m : M) (i : ι) : b.toDual m (b i) = b.repr m i :=
   b.toDual_apply_left m i
 #align basis.to_dual_eq_repr Basis.toDual_eq_repr
 
-/- warning: basis.to_dual_eq_equiv_fun -> Basis.toDual_eq_equivFun is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFunₓ'. -/
 theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.equivFun m i := by
   rw [b.equiv_fun_apply, to_dual_eq_repr]
 #align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFun
 
-/- warning: basis.to_dual_inj -> Basis.toDual_inj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_inj Basis.toDual_injₓ'. -/
 theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   by
   rw [← mem_bot R, ← b.repr.ker, mem_ker, LinearEquiv.coe_coe]
@@ -493,9 +430,6 @@ def toDualEquiv : M ≃ₗ[R] Dual R M :=
 #align basis.to_dual_equiv Basis.toDualEquiv
 -/
 
-/- warning: basis.to_dual_equiv_apply -> Basis.toDualEquiv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_dual_equiv_apply Basis.toDualEquiv_applyₓ'. -/
 -- `simps` times out when generating this
 @[simp]
 theorem toDualEquiv_apply (m : M) : b.toDualEquiv m = b.toDual m :=
@@ -509,17 +443,11 @@ def dualBasis : Basis ι R (Dual R M) :=
 #align basis.dual_basis Basis.dualBasis
 -/
 
-/- warning: basis.dual_basis_apply_self -> Basis.dualBasis_apply_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.dual_basis_apply_self Basis.dualBasis_apply_selfₓ'. -/
 -- We use `j = i` to match `basis.repr_self`
 theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1 else 0 := by
   convert b.to_dual_apply i j using 2; rw [@eq_comm _ j i]
 #align basis.dual_basis_apply_self Basis.dualBasis_apply_self
 
-/- warning: basis.total_dual_basis -> Basis.total_dualBasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.total_dual_basis Basis.total_dualBasisₓ'. -/
 theorem total_dualBasis (f : ι →₀ R) (i : ι) :
     Finsupp.total ι (Dual R M) R b.dualBasis f (b i) = f i :=
   by
@@ -531,16 +459,10 @@ theorem total_dualBasis (f : ι →₀ R) (i : ι) :
   · intro ; rw [zero_smul]
 #align basis.total_dual_basis Basis.total_dualBasis
 
-/- warning: basis.dual_basis_repr -> Basis.dualBasis_repr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.dual_basis_repr Basis.dualBasis_reprₓ'. -/
 theorem dualBasis_repr (l : Dual R M) (i : ι) : b.dualBasis.repr l i = l (b i) := by
   rw [← total_dual_basis b, Basis.total_repr b.dual_basis l]
 #align basis.dual_basis_repr Basis.dualBasis_repr
 
-/- warning: basis.dual_basis_apply -> Basis.dualBasis_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.dual_basis_apply Basis.dualBasis_applyₓ'. -/
 theorem dualBasis_apply (i : ι) (m : M) : b.dualBasis i m = b.repr m i :=
   b.toDual_apply_right i m
 #align basis.dual_basis_apply Basis.dualBasis_apply
@@ -563,16 +485,10 @@ theorem toDual_toDual : b.dualBasis.toDual.comp b.toDual = Dual.eval R M :=
 
 end Finite
 
-/- warning: basis.dual_basis_equiv_fun -> Basis.dualBasis_equivFun is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.dual_basis_equiv_fun Basis.dualBasis_equivFunₓ'. -/
 theorem dualBasis_equivFun [Fintype ι] (l : Dual R M) (i : ι) :
     b.dualBasis.equivFun l i = l (b i) := by rw [Basis.equivFun_apply, dual_basis_repr]
 #align basis.dual_basis_equiv_fun Basis.dualBasis_equivFun
 
-/- warning: basis.eval_ker -> Basis.eval_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.eval_ker Basis.eval_kerₓ'. -/
 theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   by
   rw [ker_eq_bot']
@@ -581,9 +497,6 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   exact (Basis.forall_coord_eq_zero_iff _).mp fun i => hm (b.coord i)
 #align basis.eval_ker Basis.eval_ker
 
-/- warning: basis.eval_range -> Basis.eval_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.eval_range Basis.eval_rangeₓ'. -/
 theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by
   classical
     cases nonempty_fintype ι
@@ -598,9 +511,6 @@ def evalEquiv {ι : Type _} [Finite ι] (b : Basis ι R M) : M ≃ₗ[R] Dual R
 #align basis.eval_equiv Basis.evalEquiv
 -/
 
-/- warning: basis.eval_equiv_to_linear_map -> Basis.evalEquiv_toLinearMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.eval_equiv_to_linear_map Basis.evalEquiv_toLinearMapₓ'. -/
 @[simp]
 theorem evalEquiv_toLinearMap {ι : Type _} [Finite ι] (b : Basis ι R M) :
     b.evalEquiv.toLinearMap = Dual.eval R M :=
@@ -629,9 +539,6 @@ end
 
 end CommRing
 
-/- warning: basis.total_coord -> Basis.total_coord is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.total_coord Basis.total_coordₓ'. -/
 /-- `simp` normal form version of `total_dual_basis` -/
 @[simp]
 theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b : Basis ι R M)
@@ -639,12 +546,6 @@ theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b :
   haveI := Classical.decEq ι; rw [← coe_dual_basis, total_dual_basis]
 #align basis.total_coord Basis.total_coord
 
-/- warning: basis.dual_rank_eq -> Basis.dual_rank_eq is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : Finite.{succ u3} ι], (Basis.{u3, u1, u2} ι K V (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Cardinal.lift.{u1, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Module.rank.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (CommRing.toCommSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K _inst_1) (Monoid.toMulAction.{u1} K (CommMonoid.toMonoid.{u1} K (CommRing.toCommMonoid.{u1} K _inst_1)))))))
-but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u3}} {ι : Type.{u1}} [_inst_1 : CommRing.{u2} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} K V (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : Finite.{succ u1} ι], (Basis.{u1, u2, u3} ι K V (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) -> (Eq.{max (succ (succ u2)) (succ (succ u3))} Cardinal.{max u3 u2} (Cardinal.lift.{u2, u3} (Module.rank.{u2, u3} K V (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) (Module.rank.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V (CommRing.toCommSemiring.{u2} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)))) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (smulCommClass_self.{u2, u2} K K (CommRing.toCommMonoid.{u2} K _inst_1) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)))))))))
-Case conversion may be inaccurate. Consider using '#align basis.dual_rank_eq Basis.dual_rank_eqₓ'. -/
 theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
     Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by
   classical
@@ -712,12 +613,6 @@ theorem eval_apply_injective : Function.Injective (eval K V) :=
 #align module.eval_apply_injective Module.eval_apply_injective
 -/
 
-/- warning: module.forall_dual_apply_eq_zero_iff -> Module.forall_dual_apply_eq_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall (K : Type.{u1}) {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (Eq.{succ u2} V v (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
-but is expected to have type
-  forall (K : Type.{u1}) {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) _inst_1))))))) (Eq.{succ u2} V v (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))))))
-Case conversion may be inaccurate. Consider using '#align module.forall_dual_apply_eq_zero_iff Module.forall_dual_apply_eq_zero_iffₓ'. -/
 theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v = 0) ↔ v = 0 := by
   rw [← eval_apply_eq_zero_iff K v, LinearMap.ext_iff]; rfl
 #align module.forall_dual_apply_eq_zero_iff Module.forall_dual_apply_eq_zero_iff
@@ -826,12 +721,6 @@ variable [CommRing R] [AddCommGroup M] [Module R M]
 
 variable {e : ι → M} {ε : ι → Dual R M}
 
-/- warning: module.dual_bases.coeffs -> Module.DualBases.coeffs is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> M -> (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.coeffs Module.DualBases.coeffsₓ'. -/
 /-- The coefficients of `v` on the basis `e` -/
 def coeffs [DecidableEq ι] (h : DualBases e ε) (m : M) : ι →₀ R
     where
@@ -840,35 +729,17 @@ def coeffs [DecidableEq ι] (h : DualBases e ε) (m : M) : ι →₀ R
   mem_support_toFun := by intro i; rw [Set.Finite.mem_toFinset, Set.mem_setOf_eq]
 #align module.dual_bases.coeffs Module.DualBases.coeffs
 
-/- warning: module.dual_bases.coeffs_apply -> Module.DualBases.coeffs_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.DualBases.coeffs.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h m) i) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ε i) m)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (m : M) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Module.DualBases.coeffs.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h m) i) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ε i) m)
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.coeffs_apply Module.DualBases.coeffs_applyₓ'. -/
 @[simp]
 theorem coeffs_apply [DecidableEq ι] (h : DualBases e ε) (m : M) (i : ι) : h.coeffs m i = ε i m :=
   rfl
 #align module.dual_bases.coeffs_apply Module.DualBases.coeffs_apply
 
-/- warning: module.dual_bases.lc -> Module.DualBases.lc is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}}, (ι -> M) -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> M
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}}, (ι -> M) -> (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) -> M
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.lc Module.DualBases.lcₓ'. -/
 /-- linear combinations of elements of `e`.
 This is a convenient abbreviation for `finsupp.total _ M R e l` -/
 def lc {ι} (e : ι → M) (l : ι →₀ R) : M :=
   l.Sum fun (i : ι) (a : R) => a • e i
 #align module.dual_bases.lc Module.DualBases.lc
 
-/- warning: module.dual_bases.lc_def -> Module.DualBases.lc_def is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (e : ι -> M) (l : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u2} M (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e l) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e) l)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (e : ι -> M) (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))), Eq.{succ u1} M (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _inst_3) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.total.{u3, u1, u2} ι M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e) l)
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.lc_def Module.DualBases.lc_defₓ'. -/
 theorem lc_def (e : ι → M) (l : ι →₀ R) : lc e l = Finsupp.total _ _ _ e l :=
   rfl
 #align module.dual_bases.lc_def Module.DualBases.lc_def
@@ -879,12 +750,6 @@ variable [DecidableEq ι] (h : DualBases e ε)
 
 include h
 
-/- warning: module.dual_bases.dual_lc -> Module.DualBases.dual_lc is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> (forall (l : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ε i) (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) l i))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> (forall (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ε i) (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) l i))
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.dual_lc Module.DualBases.dual_lcₓ'. -/
 theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i :=
   by
   erw [LinearMap.map_sum]
@@ -897,23 +762,11 @@ theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i :=
     simp [Finsupp.not_mem_support_iff.1 p_not_in]
 #align module.dual_bases.dual_lc Module.DualBases.dual_lc
 
-/- warning: module.dual_bases.coeffs_lc -> Module.DualBases.coeffs_lc is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (l : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.DualBases.coeffs.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) l
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))), Eq.{max (succ u2) (succ u3)} (Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Module.DualBases.coeffs.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) l
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.coeffs_lc Module.DualBases.coeffs_lcₓ'. -/
 @[simp]
 theorem coeffs_lc (l : ι →₀ R) : h.coeffs (DualBases.lc e l) = l := by ext i;
   rw [h.coeffs_apply, h.dual_lc]
 #align module.dual_bases.coeffs_lc Module.DualBases.coeffs_lc
 
-/- warning: module.dual_bases.lc_coeffs -> Module.DualBases.lc_coeffs is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (m : M), Eq.{succ u2} M (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e (Module.DualBases.coeffs.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h m)) m
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} {ι : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u1} ι] (h : Module.DualBases.{u2, u3, u1} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (m : M), Eq.{succ u3} M (Module.DualBases.lc.{u2, u3, u1} R M _inst_1 _inst_2 _inst_3 ι e (Module.DualBases.coeffs.{u2, u3, u1} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h m)) m
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.lc_coeffs Module.DualBases.lc_coeffsₓ'. -/
 /-- For any m : M n, \sum_{p ∈ Q n} (ε p m) • e p = m -/
 @[simp]
 theorem lc_coeffs (m : M) : DualBases.lc e (h.coeffs m) = m :=
@@ -937,12 +790,6 @@ def basis : Basis ι R M :=
 #align module.dual_bases.basis Module.DualBases.basis
 -/
 
-/- warning: module.dual_bases.coe_basis -> Module.DualBases.coe_basis is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε), Eq.{max (succ u3) (succ u2)} (ι -> M) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Module.DualBases.basis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h)) e
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u3}} {ι : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u3} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u2} ι] (h : Module.DualBases.{u1, u3, u2} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε), Eq.{max (succ u3) (succ u2)} (forall (a : ι), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u2, succ u3} (Basis.{u2, u1, u3} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u2, u1, u3} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (Module.DualBases.basis.{u1, u3, u2} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h)) e
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.coe_basis Module.DualBases.coe_basisₓ'. -/
 @[simp]
 theorem coe_basis : ⇑h.Basis = e := by
   ext i; rw [Basis.apply_eq_iff]; ext j
@@ -950,12 +797,6 @@ theorem coe_basis : ⇑h.Basis = e := by
   convert if_congr eq_comm rfl rfl
 #align module.dual_bases.coe_basis Module.DualBases.coe_basis
 
-/- warning: module.dual_bases.mem_of_mem_span -> Module.DualBases.mem_of_mem_span is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> (forall {H : Set.{u3} ι} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.image.{u3, u2} ι M e H))) -> (forall (i : ι), (Ne.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ε i) x) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) -> (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i H)))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> (forall {H : Set.{u3} ι} {x : M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.image.{u3, u2} ι M e H))) -> (forall (i : ι), (Ne.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ε i) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) _inst_1)))))) -> (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i H)))
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_spanₓ'. -/
 -- `convert` to get rid of a `decidable_eq` mismatch
 theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '' H)) :
     ∀ i : ι, ε i x ≠ 0 → i ∈ H := by
@@ -965,9 +806,6 @@ theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '
   rwa [← lc_def, h.dual_lc] at hi
 #align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_span
 
-/- warning: module.dual_bases.coe_dual_basis -> Module.DualBases.coe_dualBasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.dual_bases.coe_dual_basis Module.DualBases.coe_dualBasisₓ'. -/
 theorem coe_dualBasis [Fintype ι] : ⇑h.Basis.dualBasis = ε :=
   funext fun i =>
     h.Basis.ext fun j => by
@@ -999,9 +837,6 @@ theorem dualRestrict_def (W : Submodule R M) : W.dualRestrict = W.Subtype.dualMa
 #align submodule.dual_restrict_def Submodule.dualRestrict_def
 -/
 
-/- warning: submodule.dual_restrict_apply -> Submodule.dualRestrict_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_restrict_apply Submodule.dualRestrict_applyₓ'. -/
 @[simp]
 theorem dualRestrict_apply (W : Submodule R M) (φ : Module.Dual R M) (x : W) :
     W.dualRestrict φ x = φ (x : M) :=
@@ -1017,9 +852,6 @@ def dualAnnihilator {R : Type u} {M : Type v} [CommSemiring R] [AddCommMonoid M]
 #align submodule.dual_annihilator Submodule.dualAnnihilator
 -/
 
-/- warning: submodule.mem_dual_annihilator -> Submodule.mem_dualAnnihilator is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_dual_annihilator Submodule.mem_dualAnnihilatorₓ'. -/
 @[simp]
 theorem mem_dualAnnihilator (φ : Module.Dual R M) : φ ∈ W.dualAnnihilator ↔ ∀ w ∈ W, φ w = 0 :=
   by
@@ -1052,9 +884,6 @@ theorem mem_dualCoannihilator {Φ : Submodule R (Module.Dual R M)} (x : M) :
 #align submodule.mem_dual_coannihilator Submodule.mem_dualCoannihilator
 -/
 
-/- warning: submodule.dual_annihilator_gc -> Submodule.dualAnnihilator_gc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_gc Submodule.dualAnnihilator_gcₓ'. -/
 theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Module R M] :
     GaloisConnection
       (OrderDual.toDual ∘ (dualAnnihilator : Submodule R M → Submodule R (Module.Dual R M)))
@@ -1104,9 +933,6 @@ theorem dualCoannihilator_bot : (⊥ : Submodule R (Module.Dual R M)).dualCoanni
 #align submodule.dual_coannihilator_bot Submodule.dualCoannihilator_bot
 -/
 
-/- warning: submodule.dual_annihilator_anti -> Submodule.dualAnnihilator_anti is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_anti Submodule.dualAnnihilator_antiₓ'. -/
 @[mono]
 theorem dualAnnihilator_anti {U V : Submodule R M} (hUV : U ≤ V) :
     V.dualAnnihilator ≤ U.dualAnnihilator :=
@@ -1121,12 +947,6 @@ theorem dualCoannihilator_anti {U V : Submodule R (Module.Dual R M)} (hUV : U 
 #align submodule.dual_coannihilator_anti Submodule.dualCoannihilator_anti
 -/
 
-/- warning: submodule.le_dual_annihilator_dual_coannihilator -> Submodule.le_dualAnnihilator_dualCoannihilator is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3), LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))) U (Submodule.dualCoannihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3), LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))) U (Submodule.dualCoannihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U))
-Case conversion may be inaccurate. Consider using '#align submodule.le_dual_annihilator_dual_coannihilator Submodule.le_dualAnnihilator_dualCoannihilatorₓ'. -/
 theorem le_dualAnnihilator_dualCoannihilator (U : Submodule R M) :
     U ≤ U.dualAnnihilator.dualCoannihilator :=
   (dualAnnihilator_gc R M).le_u_l U
@@ -1167,25 +987,16 @@ theorem dualCoannihilator_sup_eq (U V : Submodule R (Module.Dual R M)) :
 #align submodule.dual_coannihilator_sup_eq Submodule.dualCoannihilator_sup_eq
 -/
 
-/- warning: submodule.dual_annihilator_supr_eq -> Submodule.dualAnnihilator_iSup_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eqₓ'. -/
 theorem dualAnnihilator_iSup_eq {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, U i).dualAnnihilator = ⨅ i : ι, (U i).dualAnnihilator :=
   (dualAnnihilator_gc R M).l_iSup
 #align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eq
 
-/- warning: submodule.dual_coannihilator_supr_eq -> Submodule.dualCoannihilator_iSup_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eqₓ'. -/
 theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.Dual R M)) :
     (⨆ i : ι, U i).dualCoannihilator = ⨅ i : ι, (U i).dualCoannihilator :=
   (dualAnnihilator_gc R M).u_iInf
 #align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
 
-/- warning: submodule.sup_dual_annihilator_le_inf -> Submodule.sup_dualAnnihilator_le_inf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_infₓ'. -/
 /-- See also `subspace.dual_annihilator_inf_eq` for vector subspaces. -/
 theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
     U.dualAnnihilator ⊔ V.dualAnnihilator ≤ (U ⊓ V).dualAnnihilator :=
@@ -1194,9 +1005,6 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
   apply inf_le_inf <;> exact le_dual_annihilator_dual_coannihilator _
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
 
-/- warning: submodule.supr_dual_annihilator_le_infi -> Submodule.iSup_dualAnnihilator_le_iInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.supr_dual_annihilator_le_infi Submodule.iSup_dualAnnihilator_le_iInfₓ'. -/
 /-- See also `subspace.dual_annihilator_infi_eq` for vector subspaces when `ι` is finite. -/
 theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, (U i).dualAnnihilator) ≤ (⨅ i : ι, U i).dualAnnihilator :=
@@ -1250,9 +1058,6 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
 #align subspace.dual_annihilator_dual_coannihilator_eq Subspace.dualAnnihilator_dualCoannihilator_eq
 -/
 
-/- warning: subspace.forall_mem_dual_annihilator_apply_eq_zero_iff -> Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.forall_mem_dual_annihilator_apply_eq_zero_iff Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iffₓ'. -/
 -- exact elaborates slowly
 theorem forall_mem_dualAnnihilator_apply_eq_zero_iff (W : Subspace K V) (v : V) :
     (∀ φ : Module.Dual K V, φ ∈ W.dualAnnihilator → φ v = 0) ↔ v ∈ W := by
@@ -1273,9 +1078,6 @@ def dualAnnihilatorGci (K V : Type _) [Field K] [AddCommGroup V] [Module K V] :
 #align subspace.dual_annihilator_gci Subspace.dualAnnihilatorGci
 -/
 
-/- warning: subspace.dual_annihilator_le_dual_annihilator_iff -> Subspace.dualAnnihilator_le_dualAnnihilator_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_annihilator_le_dual_annihilator_iff Subspace.dualAnnihilator_le_dualAnnihilator_iffₓ'. -/
 theorem dualAnnihilator_le_dualAnnihilator_iff {W W' : Subspace K V} :
     W.dualAnnihilator ≤ W'.dualAnnihilator ↔ W' ≤ W :=
   (dualAnnihilatorGci K V).l_le_l_iff
@@ -1303,17 +1105,11 @@ noncomputable def dualLift (W : Subspace K V) : Module.Dual K W →ₗ[K] Module
 
 variable {W : Subspace K V}
 
-/- warning: subspace.dual_lift_of_subtype -> Subspace.dualLift_of_subtype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtypeₓ'. -/
 @[simp]
 theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w := by
   erw [of_is_compl_left_apply _ w]; rfl
 #align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtype
 
-/- warning: subspace.dual_lift_of_mem -> Subspace.dualLift_of_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_mem Subspace.dualLift_of_memₓ'. -/
 theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLift φ w = φ ⟨w, hw⟩ :=
   by convert dual_lift_of_subtype ⟨w, hw⟩
 #align subspace.dual_lift_of_mem Subspace.dualLift_of_mem
@@ -1325,32 +1121,20 @@ theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.du
 #align subspace.dual_restrict_comp_dual_lift Subspace.dualRestrict_comp_dualLift
 -/
 
-/- warning: subspace.dual_restrict_left_inverse -> Subspace.dualRestrict_leftInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverseₓ'. -/
 theorem dualRestrict_leftInverse (W : Subspace K V) :
     Function.LeftInverse W.dualRestrict W.dualLift := fun x =>
   show W.dualRestrict.comp W.dualLift x = x by rw [dual_restrict_comp_dual_lift]; rfl
 #align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverse
 
-/- warning: subspace.dual_lift_right_inverse -> Subspace.dualLift_rightInverse is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_right_inverse Subspace.dualLift_rightInverseₓ'. -/
 theorem dualLift_rightInverse (W : Subspace K V) :
     Function.RightInverse W.dualLift W.dualRestrict :=
   W.dualRestrict_leftInverse
 #align subspace.dual_lift_right_inverse Subspace.dualLift_rightInverse
 
-/- warning: subspace.dual_restrict_surjective -> Subspace.dualRestrict_surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_surjective Subspace.dualRestrict_surjectiveₓ'. -/
 theorem dualRestrict_surjective : Function.Surjective W.dualRestrict :=
   W.dualLift_rightInverse.Surjective
 #align subspace.dual_restrict_surjective Subspace.dualRestrict_surjective
 
-/- warning: subspace.dual_lift_injective -> Subspace.dualLift_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_injective Subspace.dualLift_injectiveₓ'. -/
 theorem dualLift_injective : Function.Injective W.dualLift :=
   W.dualRestrict_leftInverse.Injective
 #align subspace.dual_lift_injective Subspace.dualLift_injective
@@ -1365,9 +1149,6 @@ noncomputable def quotAnnihilatorEquiv (W : Subspace K V) :
 #align subspace.quot_annihilator_equiv Subspace.quotAnnihilatorEquiv
 -/
 
-/- warning: subspace.quot_annihilator_equiv_apply -> Subspace.quotAnnihilatorEquiv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_applyₓ'. -/
 @[simp]
 theorem quotAnnihilatorEquiv_apply (W : Subspace K V) (φ : Module.Dual K V) :
     W.quotAnnihilatorEquiv (Submodule.Quotient.mk φ) = W.dualRestrict φ := by ext; rfl
@@ -1387,9 +1168,6 @@ theorem dualEquivDual_def (W : Subspace K V) :
 #align subspace.dual_equiv_dual_def Subspace.dualEquivDual_def
 -/
 
-/- warning: subspace.dual_equiv_dual_apply -> Subspace.dualEquivDual_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_equiv_dual_apply Subspace.dualEquivDual_applyₓ'. -/
 @[simp]
 theorem dualEquivDual_apply (φ : Module.Dual K W) :
     W.dualEquivDual φ = ⟨W.dualLift φ, mem_range.2 ⟨φ, rfl⟩⟩ :=
@@ -1493,9 +1271,6 @@ theorem ker_dualMap_eq_dualAnnihilator_range : f.dualMap.ker = f.range.dualAnnih
 #align linear_map.ker_dual_map_eq_dual_annihilator_range LinearMap.ker_dualMap_eq_dualAnnihilator_range
 -/
 
-/- warning: linear_map.range_dual_map_le_dual_annihilator_ker -> LinearMap.range_dualMap_le_dualAnnihilator_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_le_dual_annihilator_ker LinearMap.range_dualMap_le_dualAnnihilator_kerₓ'. -/
 theorem range_dualMap_le_dualAnnihilator_ker : f.dualMap.range ≤ f.ker.dualAnnihilator :=
   by
   rintro _ ⟨ψ, rfl⟩
@@ -1526,9 +1301,6 @@ def dualCopairing (W : Submodule R M) : W.dualAnnihilator →ₗ[R] M ⧸ W →
 #align submodule.dual_copairing Submodule.dualCopairing
 -/
 
-/- warning: submodule.dual_copairing_apply -> Submodule.dualCopairing_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_copairing_apply Submodule.dualCopairing_applyₓ'. -/
 @[simp]
 theorem dualCopairing_apply {W : Submodule R M} (φ : W.dualAnnihilator) (x : M) :
     W.dualCopairing φ (Quotient.mk x) = φ x :=
@@ -1547,18 +1319,12 @@ def dualPairing (W : Submodule R M) : Module.Dual R M ⧸ W.dualAnnihilator →
 #align submodule.dual_pairing Submodule.dualPairing
 -/
 
-/- warning: submodule.dual_pairing_apply -> Submodule.dualPairing_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_pairing_apply Submodule.dualPairing_applyₓ'. -/
 @[simp]
 theorem dualPairing_apply {W : Submodule R M} (φ : Module.Dual R M) (x : W) :
     W.dualPairing (Quotient.mk φ) x = φ x :=
   rfl
 #align submodule.dual_pairing_apply Submodule.dualPairing_apply
 
-/- warning: submodule.range_dual_map_mkq_eq -> Submodule.range_dualMap_mkQ_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.range_dual_map_mkq_eq Submodule.range_dualMap_mkQ_eqₓ'. -/
 /-- That $\operatorname{im}(q^* : (V/W)^* \to V^*) = \operatorname{ann}(W)$. -/
 theorem range_dualMap_mkQ_eq (W : Submodule R M) : W.mkQ.dualMap.range = W.dualAnnihilator :=
   by
@@ -1589,26 +1355,17 @@ def dualQuotEquivDualAnnihilator (W : Submodule R M) :
 #align submodule.dual_quot_equiv_dual_annihilator Submodule.dualQuotEquivDualAnnihilator
 -/
 
-/- warning: submodule.dual_quot_equiv_dual_annihilator_apply -> Submodule.dualQuotEquivDualAnnihilator_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_quot_equiv_dual_annihilator_apply Submodule.dualQuotEquivDualAnnihilator_applyₓ'. -/
 @[simp]
 theorem dualQuotEquivDualAnnihilator_apply (W : Submodule R M) (φ : Module.Dual R (M ⧸ W)) (x : M) :
     dualQuotEquivDualAnnihilator W φ x = φ (Quotient.mk x) :=
   rfl
 #align submodule.dual_quot_equiv_dual_annihilator_apply Submodule.dualQuotEquivDualAnnihilator_apply
 
-/- warning: submodule.dual_copairing_eq -> Submodule.dualCopairing_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_copairing_eq Submodule.dualCopairing_eqₓ'. -/
 theorem dualCopairing_eq (W : Submodule R M) :
     W.dualCopairing = (dualQuotEquivDualAnnihilator W).symm.toLinearMap :=
   rfl
 #align submodule.dual_copairing_eq Submodule.dualCopairing_eq
 
-/- warning: submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk -> Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk Submodule.dualQuotEquivDualAnnihilator_symm_apply_mkₓ'. -/
 @[simp]
 theorem dualQuotEquivDualAnnihilator_symm_apply_mk (W : Submodule R M) (φ : W.dualAnnihilator)
     (x : M) : (dualQuotEquivDualAnnihilator W).symm φ (Quotient.mk x) = φ x :=
@@ -1621,9 +1378,6 @@ namespace LinearMap
 
 open Submodule
 
-/- warning: linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective -> LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjectiveₓ'. -/
 theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
     (hf : Function.Surjective f) : f.dualMap.range = f.ker.dualAnnihilator :=
   by
@@ -1640,9 +1394,6 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
       LinearMap.quotKerEquivRange_symm_apply_image, mkq_apply]
 #align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective
 
-/- warning: linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective -> LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjectiveₓ'. -/
 -- Note, this can be specialized to the case where `R` is an injective `R`-module, or when
 -- `f.coker` is a projective `R`-module.
 theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M →ₗ[R] M')
@@ -1677,9 +1428,6 @@ theorem dualPairing_nondegenerate : (dualPairing K V₁).Nondegenerate :=
 #align linear_map.dual_pairing_nondegenerate LinearMap.dualPairing_nondegenerate
 -/
 
-/- warning: linear_map.dual_map_surjective_of_injective -> LinearMap.dualMap_surjective_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_surjective_of_injective LinearMap.dualMap_surjective_of_injectiveₓ'. -/
 theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function.Injective f) :
     Function.Surjective f.dualMap := by
   intro φ
@@ -1700,9 +1448,6 @@ theorem range_dualMap_eq_dualAnnihilator_ker (f : V₁ →ₗ[K] V₂) :
 #align linear_map.range_dual_map_eq_dual_annihilator_ker LinearMap.range_dualMap_eq_dualAnnihilator_ker
 -/
 
-/- warning: linear_map.dual_map_surjective_iff -> LinearMap.dualMap_surjective_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_surjective_iff LinearMap.dualMap_surjective_iffₓ'. -/
 /-- For vector spaces, `f.dual_map` is surjective if and only if `f` is injective -/
 @[simp]
 theorem dualMap_surjective_iff {f : V₁ →ₗ[K] V₂} :
@@ -1771,9 +1516,6 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
 #align subspace.dual_annihilator_inf_eq Subspace.dualAnnihilator_inf_eq
 -/
 
-/- warning: subspace.dual_annihilator_infi_eq -> Subspace.dualAnnihilator_iInf_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_iInf_eqₓ'. -/
 -- This is also true if `V₁` is finite dimensional since one can restrict `ι` to some subtype
 -- for which the infi and supr are the same.
 --
@@ -1843,9 +1585,6 @@ theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
 #align linear_map.finrank_range_dual_map_eq_finrank_range LinearMap.finrank_range_dualMap_eq_finrank_range
 -/
 
-/- warning: linear_map.dual_map_injective_iff -> LinearMap.dualMap_injective_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iffₓ'. -/
 /-- `f.dual_map` is injective if and only if `f` is surjective -/
 @[simp]
 theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
@@ -1861,9 +1600,6 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
     Subspace.dual_finrank_eq]
 #align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iff
 
-/- warning: linear_map.dual_map_bijective_iff -> LinearMap.dualMap_bijective_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_bijective_iff LinearMap.dualMap_bijective_iffₓ'. -/
 /-- `f.dual_map` is bijective if and only if `f` is -/
 @[simp]
 theorem dualMap_bijective_iff {f : V₁ →ₗ[K] V₂} :
@@ -1915,9 +1651,6 @@ def dualDistrib : Dual R M ⊗[R] Dual R N →ₗ[R] Dual R (M ⊗[R] N) :=
 
 variable {R M N}
 
-/- warning: tensor_product.dual_distrib_apply -> TensorProduct.dualDistrib_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_apply TensorProduct.dualDistrib_applyₓ'. -/
 @[simp]
 theorem dualDistrib_apply (f : Dual R M) (g : Dual R N) (m : M) (n : N) :
     dualDistrib R M N (f ⊗ₜ g) (m ⊗ₜ n) = f m * g n :=
@@ -1932,9 +1665,6 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N]
 
 variable [Module R M] [Module R N]
 
-/- warning: tensor_product.dual_distrib_inv_of_basis -> TensorProduct.dualDistribInvOfBasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_inv_of_basis TensorProduct.dualDistribInvOfBasisₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /-- An inverse to `dual_tensor_dual_map` given bases.
 -/
@@ -1945,9 +1675,6 @@ noncomputable def dualDistribInvOfBasis (b : Basis ι R M) (c : Basis κ R N) :
       applyₗ (c j) ∘ₗ applyₗ (b i) ∘ₗ lcurry R M N R
 #align tensor_product.dual_distrib_inv_of_basis TensorProduct.dualDistribInvOfBasis
 
-/- warning: tensor_product.dual_distrib_inv_of_basis_apply -> TensorProduct.dualDistribInvOfBasis_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_inv_of_basis_apply TensorProduct.dualDistribInvOfBasis_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem dualDistribInvOfBasis_apply (b : Basis ι R M) (c : Basis κ R N) (f : Dual R (M ⊗[R] N)) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -245,10 +245,7 @@ theorem LinearMap.dualMap_apply (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) (x :
 
 #print LinearMap.dualMap_id /-
 @[simp]
-theorem LinearMap.dualMap_id : (LinearMap.id : M₁ →ₗ[R] M₁).dualMap = LinearMap.id :=
-  by
-  ext
-  rfl
+theorem LinearMap.dualMap_id : (LinearMap.id : M₁ →ₗ[R] M₁).dualMap = LinearMap.id := by ext; rfl
 #align linear_map.dual_map_id LinearMap.dualMap_id
 -/
 
@@ -300,10 +297,7 @@ theorem LinearEquiv.dualMap_apply (f : M₁ ≃ₗ[R] M₂) (g : Dual R M₂) (x
 #print LinearEquiv.dualMap_refl /-
 @[simp]
 theorem LinearEquiv.dualMap_refl :
-    (LinearEquiv.refl R M₁).dualMap = LinearEquiv.refl R (Dual R M₁) :=
-  by
-  ext
-  rfl
+    (LinearEquiv.refl R M₁).dualMap = LinearEquiv.refl R (Dual R M₁) := by ext; rfl
 #align linear_equiv.dual_map_refl LinearEquiv.dualMap_refl
 -/
 
@@ -352,10 +346,8 @@ def toDual : M →ₗ[R] Module.Dual R M :=
 /- warning: basis.to_dual_apply -> Basis.toDual_apply is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply Basis.toDual_applyₓ'. -/
-theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0 :=
-  by
-  erw [constr_basis b, constr_basis b]
-  ac_rfl
+theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0 := by
+  erw [constr_basis b, constr_basis b]; ac_rfl
 #align basis.to_dual_apply Basis.toDual_apply
 
 /- warning: basis.to_dual_total_left -> Basis.toDual_total_left is a dubious translation:
@@ -402,10 +394,7 @@ theorem toDual_apply_right (i : ι) (m : M) : b.toDual (b i) m = b.repr m i := b
 /- warning: basis.coe_to_dual_self -> Basis.coe_toDual_self is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align basis.coe_to_dual_self Basis.coe_toDual_selfₓ'. -/
-theorem coe_toDual_self (i : ι) : b.toDual (b i) = b.Coord i :=
-  by
-  ext
-  apply to_dual_apply_right
+theorem coe_toDual_self (i : ι) : b.toDual (b i) = b.Coord i := by ext; apply to_dual_apply_right
 #align basis.coe_to_dual_self Basis.coe_toDual_self
 
 #print Basis.toDualFlip /-
@@ -524,10 +513,8 @@ def dualBasis : Basis ι R (Dual R M) :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align basis.dual_basis_apply_self Basis.dualBasis_apply_selfₓ'. -/
 -- We use `j = i` to match `basis.repr_self`
-theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1 else 0 :=
-  by
-  convert b.to_dual_apply i j using 2
-  rw [@eq_comm _ j i]
+theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1 else 0 := by
+  convert b.to_dual_apply i j using 2; rw [@eq_comm _ j i]
 #align basis.dual_basis_apply_self Basis.dualBasis_apply_self
 
 /- warning: basis.total_dual_basis -> Basis.total_dualBasis is a dubious translation:
@@ -541,8 +528,7 @@ theorem total_dualBasis (f : ι →₀ R) (i : ι) :
   ·
     simp_rw [LinearMap.smul_apply, smul_eq_mul, dual_basis_apply_self, mul_boole, Finset.sum_ite_eq,
       if_pos (Finset.mem_univ i)]
-  · intro
-    rw [zero_smul]
+  · intro ; rw [zero_smul]
 #align basis.total_dual_basis Basis.total_dualBasis
 
 /- warning: basis.dual_basis_repr -> Basis.dualBasis_repr is a dubious translation:
@@ -561,10 +547,7 @@ theorem dualBasis_apply (i : ι) (m : M) : b.dualBasis i m = b.repr m i :=
 
 #print Basis.coe_dualBasis /-
 @[simp]
-theorem coe_dualBasis : ⇑b.dualBasis = b.Coord :=
-  by
-  ext (i x)
-  apply dual_basis_apply
+theorem coe_dualBasis : ⇑b.dualBasis = b.Coord := by ext (i x); apply dual_basis_apply
 #align basis.coe_dual_basis Basis.coe_dualBasis
 -/
 
@@ -652,10 +635,8 @@ Case conversion may be inaccurate. Consider using '#align basis.total_coord Basi
 /-- `simp` normal form version of `total_dual_basis` -/
 @[simp]
 theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b : Basis ι R M)
-    (f : ι →₀ R) (i : ι) : Finsupp.total ι (Dual R M) R b.Coord f (b i) = f i :=
-  by
-  haveI := Classical.decEq ι
-  rw [← coe_dual_basis, total_dual_basis]
+    (f : ι →₀ R) (i : ι) : Finsupp.total ι (Dual R M) R b.Coord f (b i) = f i := by
+  haveI := Classical.decEq ι; rw [← coe_dual_basis, total_dual_basis]
 #align basis.total_coord Basis.total_coord
 
 /- warning: basis.dual_rank_eq -> Basis.dual_rank_eq is a dubious translation:
@@ -737,10 +718,8 @@ lean 3 declaration is
 but is expected to have type
   forall (K : Type.{u1}) {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) _inst_1))))))) (Eq.{succ u2} V v (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align module.forall_dual_apply_eq_zero_iff Module.forall_dual_apply_eq_zero_iffₓ'. -/
-theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v = 0) ↔ v = 0 :=
-  by
-  rw [← eval_apply_eq_zero_iff K v, LinearMap.ext_iff]
-  rfl
+theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v = 0) ↔ v = 0 := by
+  rw [← eval_apply_eq_zero_iff K v, LinearMap.ext_iff]; rfl
 #align module.forall_dual_apply_eq_zero_iff Module.forall_dual_apply_eq_zero_iff
 
 end
@@ -767,9 +746,7 @@ variable (K V)
 def evalEquiv [FiniteDimensional K V] : V ≃ₗ[K] Dual K (Dual K V) :=
   LinearEquiv.ofBijective
     (eval K V)-- 60x faster elaboration than using `ker_eq_bot.mp eval_ker` directly:
-    ⟨by
-      rw [← ker_eq_bot]
-      apply eval_ker K V, range_eq_top.mp erange_coe⟩
+    ⟨by rw [← ker_eq_bot]; apply eval_ker K V, range_eq_top.mp erange_coe⟩
 #align module.eval_equiv Module.evalEquiv
 -/
 
@@ -860,9 +837,7 @@ def coeffs [DecidableEq ι] (h : DualBases e ε) (m : M) : ι →₀ R
     where
   toFun i := ε i m
   support := (h.Finite m).toFinset
-  mem_support_toFun := by
-    intro i
-    rw [Set.Finite.mem_toFinset, Set.mem_setOf_eq]
+  mem_support_toFun := by intro i; rw [Set.Finite.mem_toFinset, Set.mem_setOf_eq]
 #align module.dual_bases.coeffs Module.DualBases.coeffs
 
 /- warning: module.dual_bases.coeffs_apply -> Module.DualBases.coeffs_apply is a dubious translation:
@@ -929,9 +904,7 @@ but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))), Eq.{max (succ u2) (succ u3)} (Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Module.DualBases.coeffs.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) l
 Case conversion may be inaccurate. Consider using '#align module.dual_bases.coeffs_lc Module.DualBases.coeffs_lcₓ'. -/
 @[simp]
-theorem coeffs_lc (l : ι →₀ R) : h.coeffs (DualBases.lc e l) = l :=
-  by
-  ext i
+theorem coeffs_lc (l : ι →₀ R) : h.coeffs (DualBases.lc e l) = l := by ext i;
   rw [h.coeffs_apply, h.dual_lc]
 #align module.dual_bases.coeffs_lc Module.DualBases.coeffs_lc
 
@@ -959,12 +932,8 @@ def basis : Basis ι R M :=
       invFun := lc e
       left_inv := lc_coeffs h
       right_inv := coeffs_lc h
-      map_add' := fun v w => by
-        ext i
-        exact (ε i).map_add v w
-      map_smul' := fun c v => by
-        ext i
-        exact (ε i).map_smul c v }
+      map_add' := fun v w => by ext i; exact (ε i).map_add v w
+      map_smul' := fun c v => by ext i; exact (ε i).map_smul c v }
 #align module.dual_bases.basis Module.DualBases.basis
 -/
 
@@ -976,9 +945,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align module.dual_bases.coe_basis Module.DualBases.coe_basisₓ'. -/
 @[simp]
 theorem coe_basis : ⇑h.Basis = e := by
-  ext i
-  rw [Basis.apply_eq_iff]
-  ext j
+  ext i; rw [Basis.apply_eq_iff]; ext j
   rw [h.basis_repr_apply, coeffs_apply, h.eval, Finsupp.single_apply]
   convert if_congr eq_comm rfl rfl
 #align module.dual_bases.coe_basis Module.DualBases.coe_basis
@@ -1269,12 +1236,8 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
   intro hv
   obtain ⟨W', hW⟩ := Submodule.exists_isCompl W
   obtain ⟨⟨w, w'⟩, rfl, -⟩ := exists_unique_add_of_is_compl_prod hW v
-  have hw'n : (w' : V) ∉ W := by
-    contrapose! hv
-    exact Submodule.add_mem W w.2 hv
-  have hw'nz : w' ≠ 0 := by
-    rintro rfl
-    exact hw'n (Submodule.zero_mem W)
+  have hw'n : (w' : V) ∉ W := by contrapose! hv; exact Submodule.add_mem W w.2 hv
+  have hw'nz : w' ≠ 0 := by rintro rfl; exact hw'n (Submodule.zero_mem W)
   rw [Ne.def, ← Module.forall_dual_apply_eq_zero_iff K w'] at hw'nz
   push_neg  at hw'nz
   obtain ⟨φ, hφ⟩ := hw'nz
@@ -1324,8 +1287,7 @@ theorem dualAnnihilator_inj {W W' : Subspace K V} :
   by
   constructor
   · apply (dual_annihilator_gci K V).l_injective
-  · rintro rfl
-    rfl
+  · rintro rfl; rfl
 #align subspace.dual_annihilator_inj Subspace.dualAnnihilator_inj
 -/
 
@@ -1345,10 +1307,8 @@ variable {W : Subspace K V}
 <too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtypeₓ'. -/
 @[simp]
-theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w :=
-  by
-  erw [of_is_compl_left_apply _ w]
-  rfl
+theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w := by
+  erw [of_is_compl_left_apply _ w]; rfl
 #align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtype
 
 /- warning: subspace.dual_lift_of_mem -> Subspace.dualLift_of_mem is a dubious translation:
@@ -1360,10 +1320,8 @@ theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLi
 
 #print Subspace.dualRestrict_comp_dualLift /-
 @[simp]
-theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.dualLift = 1 :=
-  by
-  ext (φ x)
-  simp
+theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.dualLift = 1 := by
+  ext (φ x); simp
 #align subspace.dual_restrict_comp_dual_lift Subspace.dualRestrict_comp_dualLift
 -/
 
@@ -1372,10 +1330,7 @@ theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.du
 Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverseₓ'. -/
 theorem dualRestrict_leftInverse (W : Subspace K V) :
     Function.LeftInverse W.dualRestrict W.dualLift := fun x =>
-  show W.dualRestrict.comp W.dualLift x = x
-    by
-    rw [dual_restrict_comp_dual_lift]
-    rfl
+  show W.dualRestrict.comp W.dualLift x = x by rw [dual_restrict_comp_dual_lift]; rfl
 #align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverse
 
 /- warning: subspace.dual_lift_right_inverse -> Subspace.dualLift_rightInverse is a dubious translation:
@@ -1415,10 +1370,7 @@ noncomputable def quotAnnihilatorEquiv (W : Subspace K V) :
 Case conversion may be inaccurate. Consider using '#align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_applyₓ'. -/
 @[simp]
 theorem quotAnnihilatorEquiv_apply (W : Subspace K V) (φ : Module.Dual K V) :
-    W.quotAnnihilatorEquiv (Submodule.Quotient.mk φ) = W.dualRestrict φ :=
-  by
-  ext
-  rfl
+    W.quotAnnihilatorEquiv (Submodule.Quotient.mk φ) = W.dualRestrict φ := by ext; rfl
 #align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_apply
 
 #print Subspace.dualEquivDual /-
@@ -1570,10 +1522,7 @@ See `subspace.dual_copairing_nondegenerate`. -/
 def dualCopairing (W : Submodule R M) : W.dualAnnihilator →ₗ[R] M ⧸ W →ₗ[R] R :=
   LinearMap.flip <|
     W.liftQ ((Module.dualPairing R M).domRestrict W.dualAnnihilator).flip
-      (by
-        intro w hw
-        ext ⟨φ, hφ⟩
-        exact (mem_dual_annihilator φ).mp hφ w hw)
+      (by intro w hw; ext ⟨φ, hφ⟩; exact (mem_dual_annihilator φ).mp hφ w hw)
 #align submodule.dual_copairing Submodule.dualCopairing
 -/
 
@@ -1636,13 +1585,7 @@ def dualQuotEquivDualAnnihilator (W : Submodule R M) :
   LinearEquiv.ofLinear
     (W.mkQ.dualMap.codRestrict W.dualAnnihilator fun φ =>
       W.range_dualMap_mkQ_eq ▸ W.mkQ.dualMap.mem_range_self φ)
-    W.dualCopairing
-    (by
-      ext
-      rfl)
-    (by
-      ext
-      rfl)
+    W.dualCopairing (by ext; rfl) (by ext; rfl)
 #align submodule.dual_quot_equiv_dual_annihilator Submodule.dualQuotEquivDualAnnihilator
 -/
 
@@ -1776,9 +1719,7 @@ open Submodule
 
 #print Subspace.dualPairing_eq /-
 theorem dualPairing_eq (W : Subspace K V₁) : W.dualPairing = W.quotAnnihilatorEquiv.toLinearMap :=
-  by
-  ext
-  rfl
+  by ext; rfl
 #align subspace.dual_pairing_eq Subspace.dualPairing_eq
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -120,10 +120,7 @@ def dualPairing (R M) [CommSemiring R] [AddCommMonoid M] [Module R M] :
 -/
 
 /- warning: module.dual_pairing_apply -> Module.dualPairing_apply is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => M -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => M -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) v x)
-but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) v) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) v x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align module.dual_pairing_apply Module.dualPairing_applyₓ'. -/
 @[simp]
 theorem dualPairing_apply (v x) : dualPairing R M v x = v x :=
@@ -147,10 +144,7 @@ def eval : M →ₗ[R] Dual R (Dual R M) :=
 -/
 
 /- warning: module.dual.eval_apply -> Module.Dual.eval_apply is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : M) (a : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (fun (_x : Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1))) => M -> (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.eval.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) a) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) a v)
-but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : M) (a : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => R) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) v) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => R) _x) (Module.Dual.instFunLikeDual.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u1 u2, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u1 u2, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.eval.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) a) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) a v)
+<too large>
 Case conversion may be inaccurate. Consider using '#align module.dual.eval_apply Module.Dual.eval_applyₓ'. -/
 @[simp]
 theorem eval_apply (v : M) (a : Dual R M) : eval R M v a = a v :=
@@ -168,10 +162,7 @@ def transpose : (M →ₗ[R] M') →ₗ[R] Dual R M' →ₗ[R] Dual R M :=
 -/
 
 /- warning: module.dual.transpose_apply -> Module.Dual.transpose_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {M' : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (u : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (l : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ (max u2 u3)) (succ (max (max u3 u1) u2 u1)), max (succ (max u2 u3)) (succ (max (max u3 u1) u2 u1))} (LinearMap.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3))) => (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) -> (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.transpose.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) u) l) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) l u)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {M' : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (u : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (l : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) l) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) u) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u1, u1, max u3 u2, max (max u2 u1) u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (smulCommClass_self.{u1, u3} R M' (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u3, max u1 u2} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u1, u2, u1} R R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max (max u1 u3) u2} R R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (smulCommClass_self.{u1, u3} R M' (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u3, max u1 u2} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u1, u2, u1} R R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.transpose.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) u) l) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) l u)
+<too large>
 Case conversion may be inaccurate. Consider using '#align module.dual.transpose_apply Module.Dual.transpose_applyₓ'. -/
 theorem transpose_apply (u : M →ₗ[R] M') (l : Dual R M') : transpose u l = l.comp u :=
   rfl
@@ -193,10 +184,7 @@ section Prod
 variable (M' : Type _) [AddCommMonoid M'] [Module R M']
 
 /- warning: module.dual_prod_dual_equiv_dual -> Module.dualProdDualEquivDual is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4], LinearEquiv.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1))
-but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4], LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align module.dual_prod_dual_equiv_dual Module.dualProdDualEquivDualₓ'. -/
 /-- Taking duals distributes over products. -/
 @[simps]
@@ -205,10 +193,7 @@ def dualProdDualEquivDual : (Module.Dual R M × Module.Dual R M') ≃ₗ[R] Modu
 #align module.dual_prod_dual_equiv_dual Module.dualProdDualEquivDual
 
 /- warning: module.dual_prod_dual_equiv_dual_apply -> Module.dualProdDualEquivDual_apply is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ψ : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (coeFn.{max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1))} (LinearEquiv.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1))) => (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) -> (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5))) (LinearEquiv.hasCoeToFun.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1)) (Module.dualProdDualEquivDual.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) (Prod.mk.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (LinearMap.coprod.{u1, u2, u3, u1} R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ ψ)
-but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ψ : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.mk.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (fun (_x : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max (max u1 u2) u3, max (max u1 u2) u3} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (SMulZeroClass.toSMul.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddMonoid.toZero.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddMonoid.toZero.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max (max u1 u2) u3, max (max u1 u2) u3} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u1 u2) u3, max (max u1 u2) u3} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.dualProdDualEquivDual.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) (Prod.mk.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (LinearMap.coprod.{u1, u2, u3, u1} R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ ψ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align module.dual_prod_dual_equiv_dual_apply Module.dualProdDualEquivDual_applyₓ'. -/
 @[simp]
 theorem dualProdDualEquivDual_apply (φ : Module.Dual R M) (ψ : Module.Dual R M') :
@@ -243,20 +228,14 @@ theorem LinearMap.dualMap_def (f : M₁ →ₗ[R] M₂) : f.dualMap = Module.Dua
 -/
 
 /- warning: linear_map.dual_map_apply' -> LinearMap.dualMap_apply' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M₁ M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M₁ M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_apply' LinearMap.dualMap_apply'ₓ'. -/
 theorem LinearMap.dualMap_apply' (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) : f.dualMap g = g.comp f :=
   rfl
 #align linear_map.dual_map_apply' LinearMap.dualMap_apply'
 
 /- warning: linear_map.dual_map_apply -> LinearMap.dualMap_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) => M₁ -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => M₂ -> R) (Module.Dual.hasCoeToFun.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₂) => R) _x) (Module.Dual.instFunLikeDual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_apply LinearMap.dualMap_applyₓ'. -/
 @[simp]
 theorem LinearMap.dualMap_apply (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
@@ -274,10 +253,7 @@ theorem LinearMap.dualMap_id : (LinearMap.id : M₁ →ₗ[R] M₁).dualMap = Li
 -/
 
 /- warning: linear_map.dual_map_comp_dual_map -> LinearMap.dualMap_comp_dualMap is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {M₃ : Type.{u4}} [_inst_6 : AddCommGroup.{u4} M₃] [_inst_7 : Module.{u1, u4} R M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6)] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₂ M₃ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_5 _inst_7), Eq.{max (succ (max u4 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u4 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u4, u1} R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u4, u1} R R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u4 u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u4, u1} R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u4, u1} R R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) (LinearMap.dualMap.{u1, u3, u4} R _inst_1 M₂ M₃ _inst_4 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7 g)) (LinearMap.dualMap.{u1, u2, u4} R _inst_1 M₁ M₃ _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7 (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M₁ M₂ M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_3 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M₁ : Type.{u3}} {M₂ : Type.{u4}} [_inst_2 : AddCommMonoid.{u3} M₁] [_inst_3 : Module.{u2, u3} R M₁ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u4} M₂] [_inst_5 : Module.{u2, u4} R M₂ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] {M₃ : Type.{u1}} [_inst_6 : AddCommGroup.{u1} M₃] [_inst_7 : Module.{u2, u1} R M₃ (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6)] (f : LinearMap.{u2, u2, u3, u4} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : LinearMap.{u2, u2, u4, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M₂ M₃ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_5 _inst_7), Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u2, u2, max u2 u1, max u2 u3} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7) (Module.Dual.{u2, u3} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (LinearMap.comp.{u2, u2, u2, max u2 u1, max u2 u4, max u2 u3} R R R (Module.Dual.{u2, u1} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7) (Module.Dual.{u2, u4} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u2, u3} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u4, u2} R R M₂ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u4, u2} R R R M₂ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.dualMap.{u2, u3, u4} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) (LinearMap.dualMap.{u2, u4, u1} R _inst_1 M₂ M₃ _inst_4 _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7 g)) (LinearMap.dualMap.{u2, u3, u1} R _inst_1 M₁ M₃ _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7 (LinearMap.comp.{u2, u2, u2, u3, u4, u1} R R R M₁ M₂ M₃ (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_3 _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) g f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_comp_dual_map LinearMap.dualMap_comp_dualMapₓ'. -/
 theorem LinearMap.dualMap_comp_dualMap {M₃ : Type _} [AddCommGroup M₃] [Module R M₃]
     (f : M₁ →ₗ[R] M₂) (g : M₂ →ₗ[R] M₃) : f.dualMap.comp g.dualMap = (g.comp f).dualMap :=
@@ -285,10 +261,7 @@ theorem LinearMap.dualMap_comp_dualMap {M₃ : Type _} [AddCommGroup M₃] [Modu
 #align linear_map.dual_map_comp_dual_map LinearMap.dualMap_comp_dualMap
 
 /- warning: linear_map.dual_map_injective_of_surjective -> LinearMap.dualMap_injective_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5}, (Function.Surjective.{succ u2, succ u3} M₁ M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5}, (Function.Surjective.{succ u2, succ u3} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_injective_of_surjective LinearMap.dualMap_injective_of_surjectiveₓ'. -/
 /-- If a linear map is surjective, then its dual is injective. -/
 theorem LinearMap.dualMap_injective_of_surjective {f : M₁ →ₗ[R] M₂} (hf : Function.Surjective f) :
@@ -316,10 +289,7 @@ def LinearEquiv.dualMap (f : M₁ ≃ₗ[R] M₂) : Dual R M₂ ≃ₗ[R] Dual R
 -/
 
 /- warning: linear_equiv.dual_map_apply -> LinearEquiv.dualMap_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) => M₁ -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearEquiv.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1)) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => M₂ -> R) (Module.Dual.hasCoeToFun.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u3, max u1 u2} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddMonoid.toZero.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u3, max u1 u2} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₂) => R) _x) (Module.Dual.instFunLikeDual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M₁) => M₂) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) R M₁ M₂ (SMulZeroClass.toSMul.{u1, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M₁ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2) (Module.toDistribMulAction.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4)) (DistribSMul.toSMulZeroClass.{u1, u3} R M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4)) (DistribMulAction.toDistribSMul.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4) (Module.toDistribMulAction.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) R M₁ M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2) (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4) (Module.toDistribMulAction.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} R M₁ M₂ (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u3, max u2 u3} R R M₁ M₂ (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_equiv.dual_map_apply LinearEquiv.dualMap_applyₓ'. -/
 @[simp]
 theorem LinearEquiv.dualMap_apply (f : M₁ ≃ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
@@ -346,10 +316,7 @@ theorem LinearEquiv.dualMap_symm {f : M₁ ≃ₗ[R] M₂} :
 -/
 
 /- warning: linear_equiv.dual_map_trans -> LinearEquiv.dualMap_trans is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {M₃ : Type.{u4}} [_inst_6 : AddCommGroup.{u4} M₃] [_inst_7 : Module.{u1, u4} R M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6)] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : LinearEquiv.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₂ M₃ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_5 _inst_7), Eq.{max (succ (max u4 u1)) (succ (max u2 u1))} (LinearEquiv.{u1, u1, max u4 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (Module.Dual.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u4, u1} R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u4, u1} R R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1))) (LinearEquiv.trans.{u1, u1, u1, max u4 u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u4, u1} R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u4, u1} R R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (LinearEquiv.dualMap.{u1, u3, u4} R _inst_1 M₂ M₃ _inst_4 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7 g) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)) (LinearEquiv.dualMap.{u1, u2, u4} R _inst_1 M₁ M₃ _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7 (LinearEquiv.trans.{u1, u1, u1, u2, u3, u4} R R R M₁ M₂ M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_3 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_1.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_2.{u1} R _inst_1) f g))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M₁ : Type.{u3}} {M₂ : Type.{u4}} [_inst_2 : AddCommMonoid.{u3} M₁] [_inst_3 : Module.{u2, u3} R M₁ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u4} M₂] [_inst_5 : Module.{u2, u4} R M₂ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] {M₃ : Type.{u1}} [_inst_6 : AddCommGroup.{u1} M₃] [_inst_7 : Module.{u2, u1} R M₃ (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6)] (f : LinearEquiv.{u2, u2, u3, u4} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : LinearEquiv.{u2, u2, u4, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M₂ M₃ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_5 _inst_7), Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearEquiv.{u2, u2, max u2 u1, max u2 u3} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Module.Dual.{u2, u1} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7) (Module.Dual.{u2, u3} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (LinearEquiv.trans.{u2, u2, u2, max u2 u1, max u2 u4, max u2 u3} R R R (Module.Dual.{u2, u1} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7) (Module.Dual.{u2, u4} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u2, u3} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u4, u2} R R M₂ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u4, u2} R R R M₂ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.dualMap.{u2, u4, u1} R _inst_1 M₂ M₃ _inst_4 _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7 g) (LinearEquiv.dualMap.{u2, u3, u4} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)) (LinearEquiv.dualMap.{u2, u3, u1} R _inst_1 M₁ M₃ _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7 (LinearEquiv.trans.{u2, u2, u2, u3, u4, u1} R R R M₁ M₂ M₃ (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_3 _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) f g))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_equiv.dual_map_trans LinearEquiv.dualMap_transₓ'. -/
 theorem LinearEquiv.dualMap_trans {M₃ : Type _} [AddCommGroup M₃] [Module R M₃] (f : M₁ ≃ₗ[R] M₂)
     (g : M₂ ≃ₗ[R] M₃) : g.dualMap.trans f.dualMap = (f.trans g).dualMap :=
@@ -383,10 +350,7 @@ def toDual : M →ₗ[R] Module.Dual R M :=
 -/
 
 /- warning: basis.to_dual_apply -> Basis.toDual_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (j : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b j)) (ite.{succ u1} R (Eq.{succ u3} ι i j) (_inst_4 i j) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (ite.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (Eq.{succ u3} ι i j) (_inst_4 i j) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) _inst_1)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply Basis.toDual_applyₓ'. -/
 theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0 :=
   by
@@ -395,10 +359,7 @@ theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0
 #align basis.to_dual_apply Basis.toDual_apply
 
 /- warning: basis.to_dual_total_left -> Basis.toDual_total_left is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b)) f)) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (a : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) f i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_total_left Basis.toDual_total_leftₓ'. -/
 @[simp]
 theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total ι M R b f) (b i) = f i :=
@@ -412,10 +373,7 @@ theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total 
 #align basis.to_dual_total_left Basis.toDual_total_left
 
 /- warning: basis.to_dual_total_right -> Basis.toDual_total_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b)) f)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (a : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) f i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_total_right Basis.toDual_total_rightₓ'. -/
 @[simp]
 theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.total ι M R b f) = f i :=
@@ -428,30 +386,21 @@ theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.
 #align basis.to_dual_total_right Basis.toDual_total_right
 
 /- warning: basis.to_dual_apply_left -> Basis.toDual_apply_left is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply_left Basis.toDual_apply_leftₓ'. -/
 theorem toDual_apply_left (m : M) (i : ι) : b.toDual m (b i) = b.repr m i := by
   rw [← b.to_dual_total_left, b.total_repr]
 #align basis.to_dual_apply_left Basis.toDual_apply_left
 
 /- warning: basis.to_dual_apply_right -> Basis.toDual_apply_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (m : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (m : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply_right Basis.toDual_apply_rightₓ'. -/
 theorem toDual_apply_right (i : ι) (m : M) : b.toDual (b i) m = b.repr m i := by
   rw [← b.to_dual_total_right, b.total_repr]
 #align basis.to_dual_apply_right Basis.toDual_apply_right
 
 /- warning: basis.coe_to_dual_self -> Basis.coe_toDual_self is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.coe_to_dual_self Basis.coe_toDual_selfₓ'. -/
 theorem coe_toDual_self (i : ι) : b.toDual (b i) = b.Coord i :=
   by
@@ -467,40 +416,28 @@ def toDualFlip (m : M) : M →ₗ[R] R :=
 -/
 
 /- warning: basis.to_dual_flip_apply -> Basis.toDualFlip_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m₁ : M) (m₂ : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Basis.toDualFlip.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b m₁) m₂) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m₂) m₁)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m₁ : M) (m₂ : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Basis.toDualFlip.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b m₁) m₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m₂) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m₂) m₁)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_flip_apply Basis.toDualFlip_applyₓ'. -/
 theorem toDualFlip_apply (m₁ m₂ : M) : b.toDualFlip m₁ m₂ = b.toDual m₂ m₁ :=
   rfl
 #align basis.to_dual_flip_apply Basis.toDualFlip_apply
 
 /- warning: basis.to_dual_eq_repr -> Basis.toDual_eq_repr is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_eq_repr Basis.toDual_eq_reprₓ'. -/
 theorem toDual_eq_repr (m : M) (i : ι) : b.toDual m (b i) = b.repr m i :=
   b.toDual_apply_left m i
 #align basis.to_dual_eq_repr Basis.toDual_eq_repr
 
 /- warning: basis.to_dual_eq_equiv_fun -> Basis.toDual_eq_equivFun is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) [_inst_5 : Fintype.{u3} ι] (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> ι -> R) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.equivFun.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 _inst_5 b) m i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) [_inst_5 : Fintype.{u3} ι] (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => ι -> R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (ι -> R) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (ι -> R) (AddMonoid.toZero.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (ι -> R) (AddMonoid.toAddZeroClass.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (ι -> R) (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (ι -> R) (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.equivFun.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 _inst_5 b) m i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFunₓ'. -/
 theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.equivFun m i := by
   rw [b.equiv_fun_apply, to_dual_eq_repr]
 #align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFun
 
 /- warning: basis.to_dual_inj -> Basis.toDual_inj is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M), (Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (OfNat.ofNat.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) 0 (OfNat.mk.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) 0 (Zero.zero.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.hasZero.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u2} M m (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M), (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) (LinearMap.instZeroLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) -> (Eq.{succ u2} M m (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_inj Basis.toDual_injₓ'. -/
 theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   by
@@ -568,10 +505,7 @@ def toDualEquiv : M ≃ₗ[R] Dual R M :=
 -/
 
 /- warning: basis.to_dual_equiv_apply -> Basis.toDualEquiv_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (m : M), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1)) (Basis.toDualEquiv.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) m) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => M -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Basis.toDual.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (m : M), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, max u1 u2} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, max u1 u2} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u2, max u1 u2} R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.toDualEquiv.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Basis.toDual.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_equiv_apply Basis.toDualEquiv_applyₓ'. -/
 -- `simps` times out when generating this
 @[simp]
@@ -587,10 +521,7 @@ def dualBasis : Basis ι R (Dual R M) :=
 -/
 
 /- warning: basis.dual_basis_apply_self -> Basis.dualBasis_apply_self is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (j : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b j)) (ite.{succ u1} R (Eq.{succ u3} ι j i) (_inst_4 j i) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) i) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (ite.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (Eq.{succ u3} ι j i) (_inst_4 j i) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) _inst_1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.dual_basis_apply_self Basis.dualBasis_apply_selfₓ'. -/
 -- We use `j = i` to match `basis.repr_self`
 theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1 else 0 :=
@@ -600,10 +531,7 @@ theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1
 #align basis.dual_basis_apply_self Basis.dualBasis_apply_self
 
 /- warning: basis.total_dual_basis -> Basis.total_dualBasis is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5))) f) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) f i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) f) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u3, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5))) f) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.total_dual_basis Basis.total_dualBasisₓ'. -/
 theorem total_dualBasis (f : ι →₀ R) (i : ι) :
     Finsupp.total ι (Dual R M) R b.dualBasis f (b i) = f i :=
@@ -618,20 +546,14 @@ theorem total_dualBasis (f : ι →₀ R) (i : ι) :
 #align basis.total_dual_basis Basis.total_dualBasis
 
 /- warning: basis.dual_basis_repr -> Basis.dualBasis_repr is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u3 u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5)) l) i) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u2), max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5)) l) i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.dual_basis_repr Basis.dualBasis_reprₓ'. -/
 theorem dualBasis_repr (l : Dual R M) (i : ι) : b.dualBasis.repr l i = l (b i) := by
   rw [← total_dual_basis b, Basis.total_repr b.dual_basis l]
 #align basis.dual_basis_repr Basis.dualBasis_repr
 
 /- warning: basis.dual_basis_apply -> Basis.dualBasis_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (m : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) m) i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (m : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) i) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) m) i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.dual_basis_apply Basis.dualBasis_applyₓ'. -/
 theorem dualBasis_apply (i : ι) (m : M) : b.dualBasis i m = b.repr m i :=
   b.toDual_apply_right i m
@@ -659,20 +581,14 @@ theorem toDual_toDual : b.dualBasis.toDual.comp b.toDual = Dual.eval R M :=
 end Finite
 
 /- warning: basis.dual_basis_equiv_fun -> Basis.dualBasis_equivFun is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Fintype.{u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> ι -> R) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u3 u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.equivFun.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) _inst_5 (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b (Finite.of_fintype.{u3} ι _inst_5))) l i) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Fintype.{u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u2), max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (ι -> R) (AddMonoid.toZero.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (ι -> R) (AddMonoid.toAddZeroClass.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.equivFun.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) _inst_5 (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b (Finite.of_fintype.{u3} ι _inst_5))) l i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.dual_basis_equiv_fun Basis.dualBasis_equivFunₓ'. -/
 theorem dualBasis_equivFun [Fintype ι] (l : Dual R M) (i : ι) :
     b.dualBasis.equivFun l i = l (b i) := by rw [Basis.equivFun_apply, dual_basis_repr]
 #align basis.dual_basis_equiv_fun Basis.dualBasis_equivFun
 
 /- warning: basis.eval_ker -> Basis.eval_ker is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, max u2 u1, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.eval.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Bot.bot.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {ι : Type.{u1}}, (Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) -> (Eq.{succ u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u3, max u2 u3, max u2 u3} R R M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u3, max u3 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u2 u3} R R M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.Dual.eval.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)) (Bot.bot.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.eval_ker Basis.eval_kerₓ'. -/
 theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   by
@@ -683,10 +599,7 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
 #align basis.eval_ker Basis.eval_ker
 
 /- warning: basis.eval_range -> Basis.eval_range is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_5 : Finite.{succ u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, u2, max u2 u1, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Top.top.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Submodule.hasTop.{u1, max u2 u1} R (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {ι : Type.{u1}} [_inst_5 : Finite.{succ u1} ι], (Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) -> (Eq.{max (succ u2) (succ u3)} (Submodule.{u2, max u2 u3} R (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.range.{u2, u2, u3, max u2 u3, max u2 u3} R R M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u3, max u3 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u2 u3} R R M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.eval.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)) (Top.top.{max u2 u3} (Submodule.{u2, max u2 u3} R (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.instTopSubmodule.{u2, max u2 u3} R (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.eval_range Basis.eval_rangeₓ'. -/
 theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by
   classical
@@ -703,10 +616,7 @@ def evalEquiv {ι : Type _} [Finite ι] (b : Basis ι R M) : M ≃ₗ[R] Dual R
 -/
 
 /- warning: basis.eval_equiv_to_linear_map -> Basis.evalEquiv_toLinearMap is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_5 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.evalEquiv._proof_4.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.evalEquiv._proof_1.{u1} R _inst_1) (Basis.evalEquiv._proof_2.{u1} R _inst_1) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.evalEquiv._proof_4.{u1} R _inst_1)) (Basis.evalEquiv.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι _inst_5 b)) (Module.Dual.eval.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {ι : Type.{u1}} [_inst_5 : Finite.{succ u1} ι] (b : Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, u3, max u2 u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearEquiv.toLinearMap.{u2, u2, u3, max u2 u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Basis.evalEquiv.{u2, u3, u1} R M _inst_1 _inst_2 _inst_3 ι _inst_5 b)) (Module.Dual.eval.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.eval_equiv_to_linear_map Basis.evalEquiv_toLinearMapₓ'. -/
 @[simp]
 theorem evalEquiv_toLinearMap {ι : Type _} [Finite ι] (b : Basis ι R M) :
@@ -737,10 +647,7 @@ end
 end CommRing
 
 /- warning: basis.total_coord -> Basis.total_coord is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (Basis.coord.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b)) f) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) f i)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) f) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u3, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b)) f) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.total_coord Basis.total_coordₓ'. -/
 /-- `simp` normal form version of `total_dual_basis` -/
 @[simp]
@@ -1092,10 +999,7 @@ theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '
 #align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_span
 
 /- warning: module.dual_bases.coe_dual_basis -> Module.DualBases.coe_dualBasis is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) [_inst_5 : Fintype.{u3} ι], Eq.{max (succ u3) (succ (max u2 u1))} (ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) (Module.DualBases.basis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h) (Finite.of_fintype.{u3} ι _inst_5))) ε
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) [_inst_5 : Fintype.{u3} ι], Eq.{max (max (succ u2) (succ u1)) (succ u3)} (forall (a : ι), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) a) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u3, max (succ u2) (succ u1)} (Basis.{u3, u2, max u1 u2} ι R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u2, max u2 u1} ι R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Basis.dualBasis.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) (Module.DualBases.basis.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h) (Finite.of_fintype.{u3} ι _inst_5))) ε
+<too large>
 Case conversion may be inaccurate. Consider using '#align module.dual_bases.coe_dual_basis Module.DualBases.coe_dualBasisₓ'. -/
 theorem coe_dualBasis [Fintype ι] : ⇑h.Basis.dualBasis = ε :=
   funext fun i =>
@@ -1129,10 +1033,7 @@ theorem dualRestrict_def (W : Submodule R M) : W.dualRestrict = W.Subtype.dualMa
 -/
 
 /- warning: submodule.dual_restrict_apply -> Submodule.dualRestrict_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.dualRestrict.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W))))) x))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) φ) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.dualRestrict.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) W)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_restrict_apply Submodule.dualRestrict_applyₓ'. -/
 @[simp]
 theorem dualRestrict_apply (W : Submodule R M) (φ : Module.Dual R M) (x : W) :
@@ -1150,10 +1051,7 @@ def dualAnnihilator {R : Type u} {M : Type v} [CommSemiring R] [AddCommMonoid M]
 -/
 
 /- warning: submodule.mem_dual_annihilator -> Submodule.mem_dualAnnihilator is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Iff (Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1)))) φ (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)) (forall (w : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) w W) -> (Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Iff (Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.setLike.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) φ (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)) (forall (w : M), (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) w W) -> (Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ w) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) _inst_1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mem_dual_annihilator Submodule.mem_dualAnnihilatorₓ'. -/
 @[simp]
 theorem mem_dualAnnihilator (φ : Module.Dual R M) : φ ∈ W.dualAnnihilator ↔ ∀ w ∈ W, φ w = 0 :=
@@ -1188,10 +1086,7 @@ theorem mem_dualCoannihilator {Φ : Submodule R (Module.Dual R M)} (x : M) :
 -/
 
 /- warning: submodule.dual_annihilator_gc -> Submodule.dualAnnihilator_gc is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_4 : CommSemiring.{u1} R] [_inst_5 : AddCommMonoid.{u2} M] [_inst_6 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5], GaloisConnection.{u2, max u2 u1} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6)))) (OrderDual.preorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))))) (Function.comp.{succ u2, succ (max u2 u1), succ (max u2 u1)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (Equiv.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) (fun (_x : Equiv.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) => (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) -> (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) (Equiv.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) (OrderDual.toDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_4 _inst_5 _inst_6)) (Function.comp.{succ (max u2 u1), succ (max u2 u1), succ u2} (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualCoannihilator._proof_1.{u1} R _inst_4))) (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (Submodule.dualCoannihilator.{u1, u2} R M _inst_4 _inst_5 _inst_6) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (Equiv.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (fun (_x : Equiv.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) => (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) -> (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Equiv.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (OrderDual.ofDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))))
-but is expected to have type
-  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_4 : CommSemiring.{u2} R] [_inst_5 : AddCommMonoid.{u1} M] [_inst_6 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5], GaloisConnection.{u1, max u2 u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (Submodule.completeLattice.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6)))) (OrderDual.preorder.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (Submodule.completeLattice.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))))) (Function.comp.{succ u1, succ (max u2 u1), succ (max u2 u1)} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (Equiv.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (fun (_x : Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) => OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) _x) (Equiv.instFunLikeEquiv.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))) (OrderDual.toDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))) (Submodule.dualAnnihilator.{u2, u1} R M _inst_4 _inst_5 _inst_6)) (Function.comp.{max (succ u2) (succ u1), max (succ u1) (succ u2), succ u1} (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (Submodule.dualCoannihilator.{u2, u1} R M _inst_4 _inst_5 _inst_6) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (Equiv.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (fun (_x : OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) => Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) _x) (Equiv.instFunLikeEquiv.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (OrderDual.ofDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_gc Submodule.dualAnnihilator_gcₓ'. -/
 theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Module R M] :
     GaloisConnection
@@ -1243,10 +1138,7 @@ theorem dualCoannihilator_bot : (⊥ : Submodule R (Module.Dual R M)).dualCoanni
 -/
 
 /- warning: submodule.dual_annihilator_anti -> Submodule.dualAnnihilator_anti is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3} {V : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))) U V) -> (LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 V) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3} {V : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))) U V) -> (LE.le.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Preorder.toLE.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Submodule.completeLattice.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 V) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_anti Submodule.dualAnnihilator_antiₓ'. -/
 @[mono]
 theorem dualAnnihilator_anti {U V : Submodule R M} (hUV : U ≤ V) :
@@ -1309,10 +1201,7 @@ theorem dualCoannihilator_sup_eq (U V : Submodule R (Module.Dual R M)) :
 -/
 
 /- warning: submodule.dual_annihilator_supr_eq -> Submodule.dualAnnihilator_iSup_eq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {ι : Type.{u3}} (U : ι -> (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)), Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (iSup.{u2, succ u3} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))) ι (fun (i : ι) => U i))) (iInf.{max u2 u1, succ u3} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.hasInf.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (U i)))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] {ι : Type.{u1}} (U : ι -> (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)), Eq.{max (succ u2) (succ u3)} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (iSup.{u3, succ u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) ι (fun (i : ι) => U i))) (iInf.{max u2 u3, succ u1} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.instInfSetSubmodule.{u2, max u2 u3} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (U i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eqₓ'. -/
 theorem dualAnnihilator_iSup_eq {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, U i).dualAnnihilator = ⨅ i : ι, (U i).dualAnnihilator :=
@@ -1320,10 +1209,7 @@ theorem dualAnnihilator_iSup_eq {ι : Type _} (U : ι → Submodule R M) :
 #align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eq
 
 /- warning: submodule.dual_coannihilator_supr_eq -> Submodule.dualCoannihilator_iSup_eq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {ι : Type.{u3}} (U : ι -> (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))))), Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.dualCoannihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (iSup.{max u2 u1, succ u3} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))))))) ι (fun (i : ι) => U i))) (iInf.{u2, succ u3} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (i : ι) => Submodule.dualCoannihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (U i)))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] {ι : Type.{u1}} (U : ι -> (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))), Eq.{succ u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Submodule.dualCoannihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (iSup.{max u2 u3, succ u1} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.completeLattice.{u2, max u2 u3} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) ι (fun (i : ι) => U i))) (iInf.{u3, succ u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Submodule.instInfSetSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) ι (fun (i : ι) => Submodule.dualCoannihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (U i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eqₓ'. -/
 theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.Dual R M)) :
     (⨆ i : ι, U i).dualCoannihilator = ⨅ i : ι, (U i).dualCoannihilator :=
@@ -1331,10 +1217,7 @@ theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.
 #align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
 
 /- warning: submodule.sup_dual_annihilator_le_inf -> Submodule.sup_dualAnnihilator_le_inf is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (V : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3), LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))))) (Sup.sup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (SemilatticeSup.toHasSup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Lattice.toSemilatticeSup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (ConditionallyCompleteLattice.toLattice.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 V)) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Inf.inf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) U V))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (V : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3), LE.le.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Preorder.toLE.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Submodule.completeLattice.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (Sup.sup.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilatticeSup.toSup.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Submodule.completeLattice.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 V)) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Inf.inf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.instInfSubmodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) U V))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_infₓ'. -/
 /-- See also `subspace.dual_annihilator_inf_eq` for vector subspaces. -/
 theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
@@ -1345,10 +1228,7 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
 
 /- warning: submodule.supr_dual_annihilator_le_infi -> Submodule.iSup_dualAnnihilator_le_iInf is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {ι : Type.{u3}} (U : ι -> (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)), LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))))) (iSup.{max u2 u1, succ u3} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (ConditionallyCompleteLattice.toHasSup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (U i))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (iInf.{u2, succ u3} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (i : ι) => U i)))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] {ι : Type.{u1}} (U : ι -> (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)), LE.le.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Preorder.toLE.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.completeLattice.{u2, max u2 u3} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))))) (iSup.{max u2 u3, succ u1} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.completeLattice.{u2, max u2 u3} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (U i))) (Submodule.dualAnnihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (iInf.{u3, succ u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Submodule.instInfSetSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) ι (fun (i : ι) => U i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.supr_dual_annihilator_le_infi Submodule.iSup_dualAnnihilator_le_iInfₓ'. -/
 /-- See also `subspace.dual_annihilator_infi_eq` for vector subspaces when `ι` is finite. -/
 theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
@@ -1408,10 +1288,7 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
 -/
 
 /- warning: subspace.forall_mem_dual_annihilator_apply_eq_zero_iff -> Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), (Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) φ (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))))) (Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v W)
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), (Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) φ (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) _inst_1)))))))) (Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v W)
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.forall_mem_dual_annihilator_apply_eq_zero_iff Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iffₓ'. -/
 -- exact elaborates slowly
 theorem forall_mem_dualAnnihilator_apply_eq_zero_iff (W : Subspace K V) (v : V) :
@@ -1434,10 +1311,7 @@ def dualAnnihilatorGci (K V : Type _) [Field K] [AddCommGroup V] [Module K V] :
 -/
 
 /- warning: subspace.dual_annihilator_le_dual_annihilator_iff -> Subspace.dualAnnihilator_le_dualAnnihilator_iff is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {W' : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Iff (LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.completeLattice.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W')) (LE.le.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) W' W)
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {W' : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Iff (LE.le.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Preorder.toLE.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.completeLattice.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W')) (LE.le.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Preorder.toLE.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) W' W)
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_annihilator_le_dual_annihilator_iff Subspace.dualAnnihilator_le_dualAnnihilator_iffₓ'. -/
 theorem dualAnnihilator_le_dualAnnihilator_iff {W W' : Subspace K V} :
     W.dualAnnihilator ≤ W'.dualAnnihilator ↔ W' ≤ W :=
@@ -1468,10 +1342,7 @@ noncomputable def dualLift (W : Subspace K V) : Module.Dual K W →ₗ[K] Module
 variable {W : Subspace K V}
 
 /- warning: subspace.dual_lift_of_subtype -> Subspace.dualLift_of_subtype is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} (w : coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W))))) w)) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) -> K) (Module.Dual.hasCoeToFun.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ w)
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} (w : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (SetLike.coe.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) W)) w)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (SetLike.coe.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) W)) w)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ w)
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtypeₓ'. -/
 @[simp]
 theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w :=
@@ -1481,10 +1352,7 @@ theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w :
 #align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtype
 
 /- warning: subspace.dual_lift_of_mem -> Subspace.dualLift_of_mem is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} {w : V} (hw : Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) w W), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) w) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) -> K) (Module.Dual.hasCoeToFun.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ (Subtype.mk.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W) w hw))
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} {w : V} (hw : Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) w W), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ (Subtype.mk.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W) w hw))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_mem Subspace.dualLift_of_memₓ'. -/
 theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLift φ w = φ ⟨w, hw⟩ :=
   by convert dual_lift_of_subtype ⟨w, hw⟩
@@ -1500,10 +1368,7 @@ theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.du
 -/
 
 /- warning: subspace.dual_restrict_left_inverse -> Subspace.dualRestrict_leftInverse is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.LeftInverse.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.LeftInverse.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverseₓ'. -/
 theorem dualRestrict_leftInverse (W : Subspace K V) :
     Function.LeftInverse W.dualRestrict W.dualLift := fun x =>
@@ -1514,10 +1379,7 @@ theorem dualRestrict_leftInverse (W : Subspace K V) :
 #align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverse
 
 /- warning: subspace.dual_lift_right_inverse -> Subspace.dualLift_rightInverse is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.RightInverse.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.RightInverse.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_right_inverse Subspace.dualLift_rightInverseₓ'. -/
 theorem dualLift_rightInverse (W : Subspace K V) :
     Function.RightInverse W.dualLift W.dualRestrict :=
@@ -1525,20 +1387,14 @@ theorem dualLift_rightInverse (W : Subspace K V) :
 #align subspace.dual_lift_right_inverse Subspace.dualLift_rightInverse
 
 /- warning: subspace.dual_restrict_surjective -> Subspace.dualRestrict_surjective is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Surjective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Surjective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_surjective Subspace.dualRestrict_surjectiveₓ'. -/
 theorem dualRestrict_surjective : Function.Surjective W.dualRestrict :=
   W.dualLift_rightInverse.Surjective
 #align subspace.dual_restrict_surjective Subspace.dualRestrict_surjective
 
 /- warning: subspace.dual_lift_injective -> Subspace.dualLift_injective is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Injective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_injective Subspace.dualLift_injectiveₓ'. -/
 theorem dualLift_injective : Function.Injective W.dualLift :=
   W.dualRestrict_leftInverse.Injective
@@ -1555,10 +1411,7 @@ noncomputable def quotAnnihilatorEquiv (W : Subspace K V) :
 -/
 
 /- warning: subspace.quot_annihilator_equiv_apply -> Subspace.quotAnnihilatorEquiv_apply is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1))) => (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1)) (Subspace.quotAnnihilatorEquiv.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.mk.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (SMulZeroClass.toSMul.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u2, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u2} K K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Subspace.quotAnnihilatorEquiv.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_applyₓ'. -/
 @[simp]
 theorem quotAnnihilatorEquiv_apply (W : Subspace K V) (φ : Module.Dual K V) :
@@ -1583,10 +1436,7 @@ theorem dualEquivDual_def (W : Subspace K V) :
 -/
 
 /- warning: subspace.dual_equiv_dual_apply -> Subspace.dualEquivDual_apply is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)), Eq.{succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1)) (Subspace.dualEquivDual.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.mk.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) x (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Iff.mpr (Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Exists.{succ (max u2 u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ))) (LinearMap.mem_range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) (Exists.intro.{succ (max u2 u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) φ (rfl.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)))))
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddMonoid.toZero.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u2, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Subspace.dualEquivDual.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.mk.{max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Iff.mpr (Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Exists.{succ (max u1 u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u1 u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) y) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ))) (LinearMap.mem_range.{max u1 u2, max u1 u2, max u1 u2, u1, u1} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) (Exists.intro.{max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u1 u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) y) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) φ (rfl.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_equiv_dual_apply Subspace.dualEquivDual_applyₓ'. -/
 @[simp]
 theorem dualEquivDual_apply (φ : Module.Dual K W) :
@@ -1692,10 +1542,7 @@ theorem ker_dualMap_eq_dualAnnihilator_range : f.dualMap.ker = f.range.dualAnnih
 -/
 
 /- warning: linear_map.range_dual_map_le_dual_annihilator_ker -> LinearMap.range_dualMap_le_dualAnnihilator_ker is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5), LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))))))) (LinearMap.range.{u1, u1, max u3 u1, max u2 u1, max (max u3 u1) u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5), LE.le.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Preorder.toLE.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Submodule.completeLattice.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (LinearMap.range.{u1, u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_le_dual_annihilator_ker LinearMap.range_dualMap_le_dualAnnihilator_kerₓ'. -/
 theorem range_dualMap_le_dualAnnihilator_ker : f.dualMap.range ≤ f.ker.dualAnnihilator :=
   by
@@ -1731,10 +1578,7 @@ def dualCopairing (W : Submodule R M) : W.dualAnnihilator →ₗ[R] M ⧸ W →
 -/
 
 /- warning: submodule.dual_copairing_apply -> Submodule.dualCopairing_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3} (φ : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1))) => (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.dualCopairing.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x)) (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) φ x)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3} (φ : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) φ) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (fun (_x : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.dualCopairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_copairing_apply Submodule.dualCopairing_applyₓ'. -/
 @[simp]
 theorem dualCopairing_apply {W : Submodule R M} (φ : W.dualAnnihilator) (x : M) :
@@ -1755,10 +1599,7 @@ def dualPairing (W : Submodule R M) : Module.Dual R M ⧸ W.dualAnnihilator →
 -/
 
 /- warning: submodule.dual_pairing_apply -> Submodule.dualPairing_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3} (φ : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1))) => (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) φ)) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) φ ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x W))))) x))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3} (φ : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.Quotient.mk.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) φ)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) (CommRing.toCommSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max (max u2 u1) u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (fun (_x : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.dualPairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) φ)) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) φ (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) W)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_pairing_apply Submodule.dualPairing_applyₓ'. -/
 @[simp]
 theorem dualPairing_apply {W : Submodule R M} (φ : Module.Dual R M) (x : W) :
@@ -1767,10 +1608,7 @@ theorem dualPairing_apply {W : Submodule R M} (φ : Module.Dual R M) (x : W) :
 #align submodule.dual_pairing_apply Submodule.dualPairing_apply
 
 /- warning: submodule.range_dual_map_mkq_eq -> Submodule.range_dualMap_mkQ_eq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap.{u1, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.mkQ.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Eq.{max (succ u2) (succ u1)} (Submodule.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.range.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearMap.dualMap.{u2, u1, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Submodule.mkQ.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.range_dual_map_mkq_eq Submodule.range_dualMap_mkQ_eqₓ'. -/
 /-- That $\operatorname{im}(q^* : (V/W)^* \to V^*) = \operatorname{ann}(W)$. -/
 theorem range_dualMap_mkQ_eq (W : Submodule R M) : W.mkQ.dualMap.range = W.dualAnnihilator :=
@@ -1809,10 +1647,7 @@ def dualQuotEquivDualAnnihilator (W : Submodule R M) :
 -/
 
 /- warning: submodule.dual_quot_equiv_dual_annihilator_apply -> Submodule.dualQuotEquivDualAnnihilator_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (φ : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) => (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) -> (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1)) (Submodule.dualQuotEquivDualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) φ (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (φ : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) φ) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toZero.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toZero.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toAddZeroClass.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) φ (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_quot_equiv_dual_annihilator_apply Submodule.dualQuotEquivDualAnnihilator_applyₓ'. -/
 @[simp]
 theorem dualQuotEquivDualAnnihilator_apply (W : Submodule R M) (φ : Module.Dual R (M ⧸ W)) (x : M) :
@@ -1821,10 +1656,7 @@ theorem dualQuotEquivDualAnnihilator_apply (W : Submodule R M) (φ : Module.Dual
 #align submodule.dual_quot_equiv_dual_annihilator_apply Submodule.dualQuotEquivDualAnnihilator_apply
 
 /- warning: submodule.dual_copairing_eq -> Submodule.dualCopairing_eq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1))) (Submodule.dualCopairing.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) (LinearEquiv.toLinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Eq.{max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualCopairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (LinearEquiv.toLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (LinearEquiv.symm.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_copairing_eq Submodule.dualCopairing_eqₓ'. -/
 theorem dualCopairing_eq (W : Submodule R M) :
     W.dualCopairing = (dualQuotEquivDualAnnihilator W).symm.toLinearMap :=
@@ -1832,10 +1664,7 @@ theorem dualCopairing_eq (W : Submodule R M) :
 #align submodule.dual_copairing_eq Submodule.dualCopairing_eq
 
 /- warning: submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk -> Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (φ : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1))) => (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)) φ) (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x)) (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) φ x)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (φ : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) φ) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (fun (_x : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toZero.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toAddZeroClass.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toZero.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearEquiv.symm.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W)) φ) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk Submodule.dualQuotEquivDualAnnihilator_symm_apply_mkₓ'. -/
 @[simp]
 theorem dualQuotEquivDualAnnihilator_symm_apply_mk (W : Submodule R M) (φ : W.dualAnnihilator)
@@ -1850,10 +1679,7 @@ namespace LinearMap
 open Submodule
 
 /- warning: linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective -> LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, max u3 u1, max u2 u1, max (max u3 u1) u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)))
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u3, max u3 u2} R (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.range.{u3, u3, max u3 u1, max u3 u2, max (max u3 u2) u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, max u1 u3, max u2 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u3, u3, max u3 u1, max u3 u2} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.dualMap.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjectiveₓ'. -/
 theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
     (hf : Function.Surjective f) : f.dualMap.range = f.ker.dualAnnihilator :=
@@ -1872,10 +1698,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
 #align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective
 
 /- warning: linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective -> LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (coeFn.{succ (max u3 u1), succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) -> (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)))) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u3 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.dualMap.{u1, u3, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) M' (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.subtype.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))))) -> (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, max u3 u1, max u2 u1, max (max u3 u1) u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)))
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u1 u3, max u1 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (fun (_x : Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) => Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, max u3 u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.dualMap.{u3, u1, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) M' (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (Submodule.subtype.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))))) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u3, max u3 u2} R (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.range.{u3, u3, max u3 u1, max u3 u2, max (max u3 u2) u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, max u1 u3, max u2 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u3, u3, max u3 u1, max u3 u2} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.dualMap.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjectiveₓ'. -/
 -- Note, this can be specialized to the case where `R` is an injective `R`-module, or when
 -- `f.coker` is a projective `R`-module.
@@ -1912,10 +1735,7 @@ theorem dualPairing_nondegenerate : (dualPairing K V₁).Nondegenerate :=
 -/
 
 /- warning: linear_map.dual_map_surjective_of_injective -> LinearMap.dualMap_surjective_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) -> (Function.Surjective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f)))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f)) -> (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_surjective_of_injective LinearMap.dualMap_surjective_of_injectiveₓ'. -/
 theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function.Injective f) :
     Function.Surjective f.dualMap := by
@@ -1938,10 +1758,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker (f : V₁ →ₗ[K] V₂) :
 -/
 
 /- warning: linear_map.dual_map_surjective_iff -> LinearMap.dualMap_surjective_iff is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Surjective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Injective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Injective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_surjective_iff LinearMap.dualMap_surjective_iffₓ'. -/
 /-- For vector spaces, `f.dual_map` is surjective if and only if `f` is injective -/
 @[simp]
@@ -2014,10 +1831,7 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
 -/
 
 /- warning: subspace.dual_annihilator_infi_eq -> Subspace.dualAnnihilator_iInf_eq is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] {ι : Type.{u3}} [_inst_6 : Finite.{succ u3} ι] (W : ι -> (Subspace.{u1, u2} K V₁ (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3)), Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (iInf.{u2, succ u3} (Subspace.{u1, u2} K V₁ (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) ι (fun (i : ι) => W i))) (iSup.{max u2 u1, succ u3} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (ConditionallyCompleteLattice.toHasSup.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.completeLattice.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (W i)))
-but is expected to have type
-  forall {K : Type.{u2}} [_inst_1 : Field.{u2} K] {V₁ : Type.{u3}} [_inst_2 : AddCommGroup.{u3} V₁] [_inst_3 : Module.{u2, u3} K V₁ (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2)] {ι : Type.{u1}} [_inst_6 : Finite.{succ u1} ι] (W : ι -> (Subspace.{u2, u3} K V₁ (Field.toDivisionRing.{u2} K _inst_1) _inst_2 _inst_3)), Eq.{max (succ u2) (succ u3)} (Submodule.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))) (Submodule.dualAnnihilator.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3 (iInf.{u3, succ u1} (Subspace.{u2, u3} K V₁ (Field.toDivisionRing.{u2} K _inst_1) _inst_2 _inst_3) (Submodule.instInfSetSubmodule.{u2, u3} K V₁ (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) ι (fun (i : ι) => W i))) (iSup.{max u2 u3, succ u1} (Submodule.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))) (Submodule.completeLattice.{u2, max u2 u3} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3 (W i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_iInf_eqₓ'. -/
 -- This is also true if `V₁` is finite dimensional since one can restrict `ι` to some subtype
 -- for which the infi and supr are the same.
@@ -2089,10 +1903,7 @@ theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
 -/
 
 /- warning: linear_map.dual_map_injective_iff -> LinearMap.dualMap_injective_iff is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Injective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Surjective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Surjective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iffₓ'. -/
 /-- `f.dual_map` is injective if and only if `f` is surjective -/
 @[simp]
@@ -2110,10 +1921,7 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
 #align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iff
 
 /- warning: linear_map.dual_map_bijective_iff -> LinearMap.dualMap_bijective_iff is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Bijective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Bijective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
-but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Bijective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Bijective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_bijective_iff LinearMap.dualMap_bijective_iffₓ'. -/
 /-- `f.dual_map` is bijective if and only if `f` is -/
 @[simp]
@@ -2167,10 +1975,7 @@ def dualDistrib : Dual R M ⊗[R] Dual R N →ₗ[R] Dual R (M ⊗[R] N) :=
 variable {R M N}
 
 /- warning: tensor_product.dual_distrib_apply -> TensorProduct.dualDistrib_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_5 : CommSemiring.{u1} R] [_inst_6 : AddCommMonoid.{u2} M] [_inst_7 : AddCommMonoid.{u3} N] [_inst_8 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6] [_inst_9 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7] (f : Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (g : Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (m : M) (n : N), Eq.{succ u1} R (coeFn.{max (succ (max u2 u3)) (succ u1), max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (fun (_x : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) => (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (coeFn.{max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1))} (LinearMap.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5))) (fun (_x : LinearMap.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5))) => (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) -> (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9))) (LinearMap.hasCoeToFun.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.dualDistrib.{u1, u2, u3} R M N _inst_5 _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.tmul.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5)) f g)) (TensorProduct.tmul.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (fun (_x : Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_5 _inst_6 _inst_8) f m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (fun (_x : Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) => N -> R) (Module.Dual.hasCoeToFun.{u1, u3} R N _inst_5 _inst_7 _inst_9) g n))
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_5 : CommSemiring.{u3} R] [_inst_6 : AddCommMonoid.{u2} M] [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6] [_inst_9 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7] (f : Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (g : Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (m : M) (n : N), Eq.{succ u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => R) (TensorProduct.tmul.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.tmul.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) f g)) (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => R) _x) (Module.Dual.instFunLikeDual.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u3, u3, max (max u1 u3) u2 u3, max (max u1 u2) u3} R R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.addCommMonoid.{u3, u3, max u2 u1, u3} R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u2 u1, u3} R R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (fun (_x : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max (max u3 u2) u1, max (max u3 u2) u1} R R (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.addCommMonoid.{u3, u3, max u2 u1, u3} R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u2 u1, u3} R R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.dualDistrib.{u3, u2, u1} R M N _inst_5 _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.tmul.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) f g)) (TensorProduct.tmul.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (HMul.hMul.{u3, u3, u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : N) => R) n) ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (instHMul.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) _inst_5))))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u3, u2} R M _inst_5 _inst_6 _inst_8) f m) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) N (fun (_x : N) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : N) => R) _x) (Module.Dual.instFunLikeDual.{u3, u1} R N _inst_5 _inst_7 _inst_9) g n))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_apply TensorProduct.dualDistrib_applyₓ'. -/
 @[simp]
 theorem dualDistrib_apply (f : Dual R M) (g : Dual R N) (m : M) (n : N) :
@@ -2187,10 +1992,7 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N]
 variable [Module R M] [Module R N]
 
 /- warning: tensor_product.dual_distrib_inv_of_basis -> TensorProduct.dualDistribInvOfBasis is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {ι : Type.{u4}} {κ : Type.{u5}} [_inst_1 : DecidableEq.{succ u4} ι] [_inst_2 : DecidableEq.{succ u5} κ] [_inst_3 : Fintype.{u4} ι] [_inst_4 : Fintype.{u5} κ] [_inst_5 : CommRing.{u1} R] [_inst_6 : AddCommGroup.{u2} M] [_inst_7 : AddCommGroup.{u3} N] [_inst_8 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6)] [_inst_9 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7)], (Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) -> (Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) -> (LinearMap.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {ι : Type.{u4}} {κ : Type.{u5}} [_inst_1 : DecidableEq.{succ u4} ι] [_inst_2 : DecidableEq.{succ u5} κ] [_inst_3 : Fintype.{u4} ι] [_inst_4 : Fintype.{u5} κ] [_inst_5 : CommRing.{u1} R] [_inst_6 : AddCommGroup.{u2} M] [_inst_7 : AddCommGroup.{u3} N] [_inst_8 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6)] [_inst_9 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7)], (Basis.{u4, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) -> (Basis.{u5, u1, u3} κ R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) -> (LinearMap.{u1, u1, max (max u3 u2) u1, max (max u3 u1) u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Module.Dual.{u1, max u3 u2} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u1 u2, max u1 u3} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u1 u2, max u1 u3} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_inv_of_basis TensorProduct.dualDistribInvOfBasisₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /-- An inverse to `dual_tensor_dual_map` given bases.
@@ -2203,10 +2005,7 @@ noncomputable def dualDistribInvOfBasis (b : Basis ι R M) (c : Basis κ R N) :
 #align tensor_product.dual_distrib_inv_of_basis TensorProduct.dualDistribInvOfBasis
 
 /- warning: tensor_product.dual_distrib_inv_of_basis_apply -> TensorProduct.dualDistribInvOfBasis_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {ι : Type.{u4}} {κ : Type.{u5}} [_inst_1 : DecidableEq.{succ u4} ι] [_inst_2 : DecidableEq.{succ u5} κ] [_inst_3 : Fintype.{u4} ι] [_inst_4 : Fintype.{u5} κ] [_inst_5 : CommRing.{u1} R] [_inst_6 : AddCommGroup.{u2} M] [_inst_7 : AddCommGroup.{u3} N] [_inst_8 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6)] [_inst_9 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7)] (b : Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (c : Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (f : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)), Eq.{succ (max (max u2 u1) u3 u1)} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (coeFn.{max (succ (max (max u2 u3) u1)) (succ (max (max u2 u1) u3 u1)), max (succ (max (max u2 u3) u1)) (succ (max (max u2 u1) u3 u1))} (LinearMap.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) (fun (_x : LinearMap.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) => (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) -> (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) (LinearMap.hasCoeToFun.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (TensorProduct.dualDistribInvOfBasis.{u1, u2, u3, u4, u5} R M N ι κ (fun (a : ι) (b : ι) => _inst_1 a b) (fun (a : κ) (b : κ) => _inst_2 a b) _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 b c) f) (Finset.sum.{max (max u2 u1) u3 u1, u4} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) ι (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Finset.univ.{u4} ι _inst_3) (fun (i : ι) => Finset.sum.{max (max u2 u1) u3 u1, u5} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) κ (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Finset.univ.{u5} κ _inst_4) (fun (j : κ) => SMul.smul.{u1, max (max u2 u1) u3 u1} R (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (TensorProduct.hasSmul.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (coeFn.{max (succ (max u2 u3)) (succ u1), max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (fun (_x : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) => (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) f (TensorProduct.tmul.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9 (coeFn.{max (succ u4) (succ u1) (succ u2), max (succ u4) (succ u2)} (Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (fun (_x : Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) => ι -> M) (FunLike.hasCoeToFun.{max (succ u4) (succ u1) (succ u2), succ u4, succ u2} (Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) ι (fun (_x : ι) => M) (Basis.funLike.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8)) b i) (coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (fun (_x : Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) => κ -> N) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) κ (fun (_x : κ) => N) (Basis.funLike.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9)) c j))) (TensorProduct.tmul.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)) (coeFn.{max (succ u4) (succ u1) (succ (max u2 u1)), max (succ u4) (succ (max u2 u1))} (Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) (fun (_x : Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8)) (FunLike.hasCoeToFun.{max (succ u4) (succ u1) (succ (max u2 u1)), succ u4, succ (max u2 u1)} (Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Basis.funLike.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5)))) (Basis.dualBasis.{u1, u2, u4} R M ι _inst_5 _inst_6 _inst_8 (fun (a : ι) (b : ι) => _inst_1 a b) b (Finite.of_fintype.{u4} ι _inst_3)) i) (coeFn.{max (succ u5) (succ u1) (succ (max u3 u1)), max (succ u5) (succ (max u3 u1))} (Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) (fun (_x : Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) => κ -> (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9)) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ (max u3 u1)), succ u5, succ (max u3 u1)} (Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) κ (fun (_x : κ) => Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Basis.funLike.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5)))) (Basis.dualBasis.{u1, u3, u5} R N κ _inst_5 _inst_7 _inst_9 (fun (a : κ) (b : κ) => _inst_2 a b) c (Finite.of_fintype.{u5} κ _inst_4)) j)))))
-but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {ι : Type.{u5}} {κ : Type.{u2}} [_inst_1 : DecidableEq.{succ u5} ι] [_inst_2 : DecidableEq.{succ u2} κ] [_inst_3 : Fintype.{u5} ι] [_inst_4 : Fintype.{u2} κ] [_inst_5 : CommRing.{u4} R] [_inst_6 : AddCommGroup.{u3} M] [_inst_7 : AddCommGroup.{u1} N] [_inst_8 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6)] [_inst_9 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7)] (b : Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (c : Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (f : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)), Eq.{max (max (succ u4) (succ u3)) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (max (succ u4) (succ u3)) (succ u1), max (max (succ u4) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max (max u1 u3) u4, max (max u1 u4) u3 u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u4} R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u4} R R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))))) (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (fun (_x : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max (max u4 u3) u1, max (max u4 u3) u1} R R (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u4} R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u4} R R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.dualDistribInvOfBasis.{u4, u3, u1, u5, u2} R M N ι κ (fun (a : ι) (b : ι) => _inst_1 a b) (fun (a : κ) (b : κ) => _inst_2 a b) _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 b c) f) (Finset.sum.{max (max u4 u3) u1, u5} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) ι (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Finset.univ.{u5} ι _inst_3) (fun (i : ι) => Finset.sum.{max (max u4 u3) u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) κ (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Finset.univ.{u2} κ _inst_4) (fun (j : κ) => HSMul.hSMul.{u4, max (max u4 u1) u4 u3, max (max u4 u3) u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5)))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) (instHSMul.{u4, max (max u4 u3) u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5)))))) (TensorProduct.instSMulTensorProduct.{u4, max u4 u3, max u4 u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u4} (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (fun (_x : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) _x) (Module.Dual.instFunLikeDual.{u4, max u3 u1} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) f (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (_x : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) _x) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.tmul.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, max (succ u4) (succ u3)} (Basis.{u5, u4, max u3 u4} ι R (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) _x) (Basis.funLike.{u5, u4, max u4 u3} ι R (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Basis.dualBasis.{u4, u3, u5} R M ι _inst_5 _inst_6 _inst_8 (fun (a : ι) (b : ι) => _inst_1 a b) b (Finite.of_fintype.{u5} ι _inst_3)) i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, max (succ u4) (succ u1)} (Basis.{u2, u4, max u1 u4} κ R (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) κ (fun (_x : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) _x) (Basis.funLike.{u2, u4, max u4 u1} κ R (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Basis.dualBasis.{u4, u1, u2} R N κ _inst_5 _inst_7 _inst_9 (fun (a : κ) (b : κ) => _inst_2 a b) c (Finite.of_fintype.{u2} κ _inst_4)) j)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_inv_of_basis_apply TensorProduct.dualDistribInvOfBasis_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -123,7 +123,7 @@ def dualPairing (R M) [CommSemiring R] [AddCommMonoid M] [Module R M] :
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => M -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => M -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) v x)
 but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) v) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) v x)
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) v) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) v x)
 Case conversion may be inaccurate. Consider using '#align module.dual_pairing_apply Module.dualPairing_applyₓ'. -/
 @[simp]
 theorem dualPairing_apply (v x) : dualPairing R M v x = v x :=
@@ -150,7 +150,7 @@ def eval : M →ₗ[R] Dual R (Dual R M) :=
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : M) (a : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (fun (_x : Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1))) => M -> (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.eval.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) a) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) a v)
 but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : M) (a : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => R) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) v) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => R) _x) (Module.Dual.instFunLikeDual.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u1 u2, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u1 u2, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.eval.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) a) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) a v)
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : M) (a : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => R) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) v) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => R) _x) (Module.Dual.instFunLikeDual.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u1 u2, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u1 u2, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.eval.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) a) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) a v)
 Case conversion may be inaccurate. Consider using '#align module.dual.eval_apply Module.Dual.eval_applyₓ'. -/
 @[simp]
 theorem eval_apply (v : M) (a : Dual R M) : eval R M v a = a v :=
@@ -171,7 +171,7 @@ def transpose : (M →ₗ[R] M') →ₗ[R] Dual R M' →ₗ[R] Dual R M :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {M' : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (u : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (l : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ (max u2 u3)) (succ (max (max u3 u1) u2 u1)), max (succ (max u2 u3)) (succ (max (max u3 u1) u2 u1))} (LinearMap.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3))) => (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) -> (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.transpose.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) u) l) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) l u)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {M' : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (u : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (l : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) l) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) u) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u1, u1, max u3 u2, max (max u2 u1) u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (smulCommClass_self.{u1, u3} R M' (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u3, max u1 u2} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u1, u2, u1} R R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max (max u1 u3) u2} R R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (smulCommClass_self.{u1, u3} R M' (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u3, max u1 u2} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u1, u2, u1} R R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.transpose.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) u) l) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) l u)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {M' : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (u : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (l : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) l) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) u) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u1, u1, max u3 u2, max (max u2 u1) u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (smulCommClass_self.{u1, u3} R M' (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u3, max u1 u2} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u1, u2, u1} R R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max (max u1 u3) u2} R R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (smulCommClass_self.{u1, u3} R M' (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u3, max u1 u2} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u1, u2, u1} R R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.transpose.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) u) l) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) l u)
 Case conversion may be inaccurate. Consider using '#align module.dual.transpose_apply Module.Dual.transpose_applyₓ'. -/
 theorem transpose_apply (u : M →ₗ[R] M') (l : Dual R M') : transpose u l = l.comp u :=
   rfl
@@ -208,7 +208,7 @@ def dualProdDualEquivDual : (Module.Dual R M × Module.Dual R M') ≃ₗ[R] Modu
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ψ : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (coeFn.{max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1))} (LinearEquiv.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1))) => (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) -> (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5))) (LinearEquiv.hasCoeToFun.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1)) (Module.dualProdDualEquivDual.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) (Prod.mk.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (LinearMap.coprod.{u1, u2, u3, u1} R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ ψ)
 but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ψ : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.mk.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (fun (_x : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max (max u1 u2) u3, max (max u1 u2) u3} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (SMulZeroClass.toSMul.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddMonoid.toZero.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddMonoid.toZero.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max (max u1 u2) u3, max (max u1 u2) u3} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u1 u2) u3, max (max u1 u2) u3} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.dualProdDualEquivDual.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) (Prod.mk.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (LinearMap.coprod.{u1, u2, u3, u1} R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ ψ)
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ψ : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.mk.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (fun (_x : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max (max u1 u2) u3, max (max u1 u2) u3} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (SMulZeroClass.toSMul.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddMonoid.toZero.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddMonoid.toZero.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max (max u1 u2) u3, max (max u1 u2) u3} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u1 u2) u3, max (max u1 u2) u3} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.dualProdDualEquivDual.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) (Prod.mk.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (LinearMap.coprod.{u1, u2, u3, u1} R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ ψ)
 Case conversion may be inaccurate. Consider using '#align module.dual_prod_dual_equiv_dual_apply Module.dualProdDualEquivDual_applyₓ'. -/
 @[simp]
 theorem dualProdDualEquivDual_apply (φ : Module.Dual R M) (ψ : Module.Dual R M') :
@@ -246,7 +246,7 @@ theorem LinearMap.dualMap_def (f : M₁ →ₗ[R] M₂) : f.dualMap = Module.Dua
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M₁ M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M₁ M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M₁ M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f)
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_apply' LinearMap.dualMap_apply'ₓ'. -/
 theorem LinearMap.dualMap_apply' (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) : f.dualMap g = g.comp f :=
   rfl
@@ -256,7 +256,7 @@ theorem LinearMap.dualMap_apply' (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) : f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) => M₁ -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => M₂ -> R) (Module.Dual.hasCoeToFun.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₂) => R) _x) (Module.Dual.instFunLikeDual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₂) => R) _x) (Module.Dual.instFunLikeDual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x))
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_apply LinearMap.dualMap_applyₓ'. -/
 @[simp]
 theorem LinearMap.dualMap_apply (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
@@ -288,7 +288,7 @@ theorem LinearMap.dualMap_comp_dualMap {M₃ : Type _} [AddCommGroup M₃] [Modu
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5}, (Function.Surjective.{succ u2, succ u3} M₁ M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5}, (Function.Surjective.{succ u2, succ u3} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5}, (Function.Surjective.{succ u2, succ u3} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)))
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_injective_of_surjective LinearMap.dualMap_injective_of_surjectiveₓ'. -/
 /-- If a linear map is surjective, then its dual is injective. -/
 theorem LinearMap.dualMap_injective_of_surjective {f : M₁ →ₗ[R] M₂} (hf : Function.Surjective f) :
@@ -319,7 +319,7 @@ def LinearEquiv.dualMap (f : M₁ ≃ₗ[R] M₂) : Dual R M₂ ≃ₗ[R] Dual R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) => M₁ -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearEquiv.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1)) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => M₂ -> R) (Module.Dual.hasCoeToFun.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u3, max u1 u2} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddMonoid.toZero.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u3, max u1 u2} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₂) => R) _x) (Module.Dual.instFunLikeDual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M₁) => M₂) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) R M₁ M₂ (SMulZeroClass.toSMul.{u1, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M₁ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2) (Module.toDistribMulAction.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4)) (DistribSMul.toSMulZeroClass.{u1, u3} R M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4)) (DistribMulAction.toDistribSMul.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4) (Module.toDistribMulAction.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) R M₁ M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2) (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4) (Module.toDistribMulAction.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} R M₁ M₂ (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u3, max u2 u3} R R M₁ M₂ (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u3, max u1 u2} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddMonoid.toZero.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u3, max u1 u2} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₂) => R) _x) (Module.Dual.instFunLikeDual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M₁) => M₂) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) R M₁ M₂ (SMulZeroClass.toSMul.{u1, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M₁ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2) (Module.toDistribMulAction.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4)) (DistribSMul.toSMulZeroClass.{u1, u3} R M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4)) (DistribMulAction.toDistribSMul.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4) (Module.toDistribMulAction.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) R M₁ M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2) (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4) (Module.toDistribMulAction.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} R M₁ M₂ (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u3, max u2 u3} R R M₁ M₂ (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.dual_map_apply LinearEquiv.dualMap_applyₓ'. -/
 @[simp]
 theorem LinearEquiv.dualMap_apply (f : M₁ ≃ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
@@ -386,7 +386,7 @@ def toDual : M →ₗ[R] Module.Dual R M :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (j : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b j)) (ite.{succ u1} R (Eq.{succ u3} ι i j) (_inst_4 i j) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (ite.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (Eq.{succ u3} ι i j) (_inst_4 i j) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) _inst_1)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (ite.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (Eq.{succ u3} ι i j) (_inst_4 i j) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply Basis.toDual_applyₓ'. -/
 theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0 :=
   by
@@ -398,7 +398,7 @@ theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b)) f)) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (a : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) f i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (a : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) f i)
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_total_left Basis.toDual_total_leftₓ'. -/
 @[simp]
 theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total ι M R b f) (b i) = f i :=
@@ -415,7 +415,7 @@ theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b)) f)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (a : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) f i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (a : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) f i)
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_total_right Basis.toDual_total_rightₓ'. -/
 @[simp]
 theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.total ι M R b f) = f i :=
@@ -431,7 +431,7 @@ theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply_left Basis.toDual_apply_leftₓ'. -/
 theorem toDual_apply_left (m : M) (i : ι) : b.toDual m (b i) = b.repr m i := by
   rw [← b.to_dual_total_left, b.total_repr]
@@ -441,7 +441,7 @@ theorem toDual_apply_left (m : M) (i : ι) : b.toDual m (b i) = b.repr m i := by
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (m : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (m : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (m : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply_right Basis.toDual_apply_rightₓ'. -/
 theorem toDual_apply_right (i : ι) (m : M) : b.toDual (b i) m = b.repr m i := by
   rw [← b.to_dual_total_right, b.total_repr]
@@ -451,7 +451,7 @@ theorem toDual_apply_right (i : ι) (m : M) : b.toDual (b i) m = b.repr m i := b
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b i)
 Case conversion may be inaccurate. Consider using '#align basis.coe_to_dual_self Basis.coe_toDual_selfₓ'. -/
 theorem coe_toDual_self (i : ι) : b.toDual (b i) = b.Coord i :=
   by
@@ -470,7 +470,7 @@ def toDualFlip (m : M) : M →ₗ[R] R :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m₁ : M) (m₂ : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Basis.toDualFlip.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b m₁) m₂) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m₂) m₁)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m₁ : M) (m₂ : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Basis.toDualFlip.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b m₁) m₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m₂) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m₂) m₁)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m₁ : M) (m₂ : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Basis.toDualFlip.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b m₁) m₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m₂) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m₂) m₁)
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_flip_apply Basis.toDualFlip_applyₓ'. -/
 theorem toDualFlip_apply (m₁ m₂ : M) : b.toDualFlip m₁ m₂ = b.toDual m₂ m₁ :=
   rfl
@@ -480,7 +480,7 @@ theorem toDualFlip_apply (m₁ m₂ : M) : b.toDualFlip m₁ m₂ = b.toDual m
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_eq_repr Basis.toDual_eq_reprₓ'. -/
 theorem toDual_eq_repr (m : M) (i : ι) : b.toDual m (b i) = b.repr m i :=
   b.toDual_apply_left m i
@@ -490,7 +490,7 @@ theorem toDual_eq_repr (m : M) (i : ι) : b.toDual m (b i) = b.repr m i :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) [_inst_5 : Fintype.{u3} ι] (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> ι -> R) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.equivFun.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 _inst_5 b) m i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) [_inst_5 : Fintype.{u3} ι] (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => ι -> R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (ι -> R) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (ι -> R) (AddMonoid.toZero.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (ι -> R) (AddMonoid.toAddZeroClass.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (ι -> R) (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (ι -> R) (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.equivFun.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 _inst_5 b) m i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) [_inst_5 : Fintype.{u3} ι] (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => ι -> R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (ι -> R) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (ι -> R) (AddMonoid.toZero.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (ι -> R) (AddMonoid.toAddZeroClass.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (ι -> R) (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (ι -> R) (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.equivFun.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 _inst_5 b) m i)
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFunₓ'. -/
 theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.equivFun m i := by
   rw [b.equiv_fun_apply, to_dual_eq_repr]
@@ -500,7 +500,7 @@ theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M), (Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (OfNat.ofNat.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) 0 (OfNat.mk.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) 0 (Zero.zero.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.hasZero.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u2} M m (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M), (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) (LinearMap.instZeroLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) -> (Eq.{succ u2} M m (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M), (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) (LinearMap.instZeroLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) -> (Eq.{succ u2} M m (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_inj Basis.toDual_injₓ'. -/
 theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   by
@@ -571,7 +571,7 @@ def toDualEquiv : M ≃ₗ[R] Dual R M :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (m : M), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1)) (Basis.toDualEquiv.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) m) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => M -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Basis.toDual.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (m : M), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, max u1 u2} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, max u1 u2} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u2, max u1 u2} R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.toDualEquiv.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Basis.toDual.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (m : M), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, max u1 u2} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, max u1 u2} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u2, max u1 u2} R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.toDualEquiv.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Basis.toDual.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m)
 Case conversion may be inaccurate. Consider using '#align basis.to_dual_equiv_apply Basis.toDualEquiv_applyₓ'. -/
 -- `simps` times out when generating this
 @[simp]
@@ -603,7 +603,7 @@ theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5))) f) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) f i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) f) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u3, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5))) f) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) f) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u3, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5))) f) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f i)
 Case conversion may be inaccurate. Consider using '#align basis.total_dual_basis Basis.total_dualBasisₓ'. -/
 theorem total_dualBasis (f : ι →₀ R) (i : ι) :
     Finsupp.total ι (Dual R M) R b.dualBasis f (b i) = f i :=
@@ -621,7 +621,7 @@ theorem total_dualBasis (f : ι →₀ R) (i : ι) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u3 u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5)) l) i) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u2), max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5)) l) i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i))
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u2), max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5)) l) i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i))
 Case conversion may be inaccurate. Consider using '#align basis.dual_basis_repr Basis.dualBasis_reprₓ'. -/
 theorem dualBasis_repr (l : Dual R M) (i : ι) : b.dualBasis.repr l i = l (b i) := by
   rw [← total_dual_basis b, Basis.total_repr b.dual_basis l]
@@ -631,7 +631,7 @@ theorem dualBasis_repr (l : Dual R M) (i : ι) : b.dualBasis.repr l i = l (b i)
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (m : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) m) i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (m : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) i) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) m) i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (m : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) i) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) m) i)
 Case conversion may be inaccurate. Consider using '#align basis.dual_basis_apply Basis.dualBasis_applyₓ'. -/
 theorem dualBasis_apply (i : ι) (m : M) : b.dualBasis i m = b.repr m i :=
   b.toDual_apply_right i m
@@ -662,7 +662,7 @@ end Finite
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Fintype.{u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> ι -> R) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u3 u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.equivFun.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) _inst_5 (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b (Finite.of_fintype.{u3} ι _inst_5))) l i) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Fintype.{u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u2), max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (ι -> R) (AddMonoid.toZero.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (ι -> R) (AddMonoid.toAddZeroClass.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.equivFun.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) _inst_5 (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b (Finite.of_fintype.{u3} ι _inst_5))) l i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i))
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Fintype.{u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u2), max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (ι -> R) (AddMonoid.toZero.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (ι -> R) (AddMonoid.toAddZeroClass.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.equivFun.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) _inst_5 (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b (Finite.of_fintype.{u3} ι _inst_5))) l i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i))
 Case conversion may be inaccurate. Consider using '#align basis.dual_basis_equiv_fun Basis.dualBasis_equivFunₓ'. -/
 theorem dualBasis_equivFun [Fintype ι] (l : Dual R M) (i : ι) :
     b.dualBasis.equivFun l i = l (b i) := by rw [Basis.equivFun_apply, dual_basis_repr]
@@ -740,7 +740,7 @@ end CommRing
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (Basis.coord.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b)) f) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) f i)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) f) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u3, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b)) f) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f i)
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) f) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u3, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b)) f) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f i)
 Case conversion may be inaccurate. Consider using '#align basis.total_coord Basis.total_coordₓ'. -/
 /-- `simp` normal form version of `total_dual_basis` -/
 @[simp]
@@ -985,7 +985,7 @@ def lc {ι} (e : ι → M) (l : ι →₀ R) : M :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (e : ι -> M) (l : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u2} M (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e l) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e) l)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (e : ι -> M) (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))), Eq.{succ u1} M (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _inst_3) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.total.{u3, u1, u2} ι M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e) l)
+  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (e : ι -> M) (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))), Eq.{succ u1} M (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _inst_3) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.total.{u3, u1, u2} ι M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e) l)
 Case conversion may be inaccurate. Consider using '#align module.dual_bases.lc_def Module.DualBases.lc_defₓ'. -/
 theorem lc_def (e : ι → M) (l : ι →₀ R) : lc e l = Finsupp.total _ _ _ e l :=
   rfl
@@ -1132,7 +1132,7 @@ theorem dualRestrict_def (W : Submodule R M) : W.dualRestrict = W.Subtype.dualMa
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.dualRestrict.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W))))) x))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) φ) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.dualRestrict.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) W)) x))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) φ) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.dualRestrict.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) W)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.dual_restrict_apply Submodule.dualRestrict_applyₓ'. -/
 @[simp]
 theorem dualRestrict_apply (W : Submodule R M) (φ : Module.Dual R M) (x : W) :
@@ -1471,7 +1471,7 @@ variable {W : Subspace K V}
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} (w : coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W))))) w)) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) -> K) (Module.Dual.hasCoeToFun.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ w)
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} (w : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (SetLike.coe.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) W)) w)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (SetLike.coe.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) W)) w)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ w)
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} (w : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (SetLike.coe.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) W)) w)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (SetLike.coe.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) W)) w)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ w)
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtypeₓ'. -/
 @[simp]
 theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w :=
@@ -1484,7 +1484,7 @@ theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} {w : V} (hw : Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) w W), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) w) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) -> K) (Module.Dual.hasCoeToFun.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ (Subtype.mk.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W) w hw))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} {w : V} (hw : Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) w W), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ (Subtype.mk.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W) w hw))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} {w : V} (hw : Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) w W), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ (Subtype.mk.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W) w hw))
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_mem Subspace.dualLift_of_memₓ'. -/
 theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLift φ w = φ ⟨w, hw⟩ :=
   by convert dual_lift_of_subtype ⟨w, hw⟩
@@ -1503,7 +1503,7 @@ theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.du
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.LeftInverse.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.LeftInverse.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.LeftInverse.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
 Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverseₓ'. -/
 theorem dualRestrict_leftInverse (W : Subspace K V) :
     Function.LeftInverse W.dualRestrict W.dualLift := fun x =>
@@ -1517,7 +1517,7 @@ theorem dualRestrict_leftInverse (W : Subspace K V) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.RightInverse.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.RightInverse.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.RightInverse.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_right_inverse Subspace.dualLift_rightInverseₓ'. -/
 theorem dualLift_rightInverse (W : Subspace K V) :
     Function.RightInverse W.dualLift W.dualRestrict :=
@@ -1528,7 +1528,7 @@ theorem dualLift_rightInverse (W : Subspace K V) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Surjective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Surjective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Surjective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
 Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_surjective Subspace.dualRestrict_surjectiveₓ'. -/
 theorem dualRestrict_surjective : Function.Surjective W.dualRestrict :=
   W.dualLift_rightInverse.Surjective
@@ -1538,7 +1538,7 @@ theorem dualRestrict_surjective : Function.Surjective W.dualRestrict :=
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Injective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
 Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_injective Subspace.dualLift_injectiveₓ'. -/
 theorem dualLift_injective : Function.Injective W.dualLift :=
   W.dualRestrict_leftInverse.Injective
@@ -1558,7 +1558,7 @@ noncomputable def quotAnnihilatorEquiv (W : Subspace K V) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1))) => (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1)) (Subspace.quotAnnihilatorEquiv.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.mk.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (SMulZeroClass.toSMul.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u2, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u2} K K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Subspace.quotAnnihilatorEquiv.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.mk.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (SMulZeroClass.toSMul.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u2, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u2} K K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Subspace.quotAnnihilatorEquiv.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)
 Case conversion may be inaccurate. Consider using '#align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_applyₓ'. -/
 @[simp]
 theorem quotAnnihilatorEquiv_apply (W : Subspace K V) (φ : Module.Dual K V) :
@@ -1586,7 +1586,7 @@ theorem dualEquivDual_def (W : Subspace K V) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)), Eq.{succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1)) (Subspace.dualEquivDual.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.mk.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) x (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Iff.mpr (Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Exists.{succ (max u2 u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ))) (LinearMap.mem_range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) (Exists.intro.{succ (max u2 u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) φ (rfl.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddMonoid.toZero.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u2, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Subspace.dualEquivDual.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.mk.{max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Iff.mpr (Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Exists.{succ (max u1 u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u1 u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) y) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ))) (LinearMap.mem_range.{max u1 u2, max u1 u2, max u1 u2, u1, u1} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) (Exists.intro.{max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u1 u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) y) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) φ (rfl.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddMonoid.toZero.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u2, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Subspace.dualEquivDual.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.mk.{max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Iff.mpr (Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Exists.{succ (max u1 u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u1 u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) y) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ))) (LinearMap.mem_range.{max u1 u2, max u1 u2, max u1 u2, u1, u1} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) (Exists.intro.{max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u1 u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) y) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) φ (rfl.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)))))
 Case conversion may be inaccurate. Consider using '#align subspace.dual_equiv_dual_apply Subspace.dualEquivDual_applyₓ'. -/
 @[simp]
 theorem dualEquivDual_apply (φ : Module.Dual K W) :
@@ -1734,7 +1734,7 @@ def dualCopairing (W : Submodule R M) : W.dualAnnihilator →ₗ[R] M ⧸ W →
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3} (φ : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1))) => (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.dualCopairing.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x)) (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) φ x)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3} (φ : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) φ) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (fun (_x : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.dualCopairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ x)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3} (φ : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) φ) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (fun (_x : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.dualCopairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ x)
 Case conversion may be inaccurate. Consider using '#align submodule.dual_copairing_apply Submodule.dualCopairing_applyₓ'. -/
 @[simp]
 theorem dualCopairing_apply {W : Submodule R M} (φ : W.dualAnnihilator) (x : M) :
@@ -1758,7 +1758,7 @@ def dualPairing (W : Submodule R M) : Module.Dual R M ⧸ W.dualAnnihilator →
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3} (φ : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1))) => (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) φ)) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) φ ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x W))))) x))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3} (φ : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.Quotient.mk.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) φ)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) (CommRing.toCommSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max (max u2 u1) u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (fun (_x : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.dualPairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) φ)) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) φ (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) W)) x))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3} (φ : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.Quotient.mk.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) φ)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) (CommRing.toCommSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max (max u2 u1) u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (fun (_x : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.dualPairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) φ)) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) φ (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) W)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.dual_pairing_apply Submodule.dualPairing_applyₓ'. -/
 @[simp]
 theorem dualPairing_apply {W : Submodule R M} (φ : Module.Dual R M) (x : W) :
@@ -1812,7 +1812,7 @@ def dualQuotEquivDualAnnihilator (W : Submodule R M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (φ : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) => (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) -> (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1)) (Submodule.dualQuotEquivDualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) φ (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (φ : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) φ) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toZero.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toZero.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toAddZeroClass.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) φ (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (φ : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) φ) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toZero.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toZero.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toAddZeroClass.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) φ (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x))
 Case conversion may be inaccurate. Consider using '#align submodule.dual_quot_equiv_dual_annihilator_apply Submodule.dualQuotEquivDualAnnihilator_applyₓ'. -/
 @[simp]
 theorem dualQuotEquivDualAnnihilator_apply (W : Submodule R M) (φ : Module.Dual R (M ⧸ W)) (x : M) :
@@ -1835,7 +1835,7 @@ theorem dualCopairing_eq (W : Submodule R M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (φ : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1))) => (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)) φ) (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x)) (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) φ x)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (φ : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) φ) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (fun (_x : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toZero.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toAddZeroClass.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toZero.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearEquiv.symm.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W)) φ) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ x)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (φ : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) φ) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (fun (_x : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toZero.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toAddZeroClass.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toZero.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearEquiv.symm.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W)) φ) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ x)
 Case conversion may be inaccurate. Consider using '#align submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk Submodule.dualQuotEquivDualAnnihilator_symm_apply_mkₓ'. -/
 @[simp]
 theorem dualQuotEquivDualAnnihilator_symm_apply_mk (W : Submodule R M) (φ : W.dualAnnihilator)
@@ -1853,7 +1853,7 @@ open Submodule
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, max u3 u1, max u2 u1, max (max u3 u1) u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)))
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u3, max u3 u2} R (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.range.{u3, u3, max u3 u1, max u3 u2, max (max u3 u2) u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, max u1 u3, max u2 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u3, u3, max u3 u1, max u3 u2} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.dualMap.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)))
+  forall {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u3, max u3 u2} R (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.range.{u3, u3, max u3 u1, max u3 u2, max (max u3 u2) u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, max u1 u3, max u2 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u3, u3, max u3 u1, max u3 u2} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.dualMap.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)))
 Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjectiveₓ'. -/
 theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
     (hf : Function.Surjective f) : f.dualMap.range = f.ker.dualAnnihilator :=
@@ -1875,7 +1875,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (coeFn.{succ (max u3 u1), succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) -> (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)))) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u3 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.dualMap.{u1, u3, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) M' (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.subtype.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))))) -> (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, max u3 u1, max u2 u1, max (max u3 u1) u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)))
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u1 u3, max u1 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (fun (_x : Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) => Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, max u3 u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.dualMap.{u3, u1, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) M' (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (Submodule.subtype.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))))) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u3, max u3 u2} R (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.range.{u3, u3, max u3 u1, max u3 u2, max (max u3 u2) u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, max u1 u3, max u2 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u3, u3, max u3 u1, max u3 u2} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.dualMap.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)))
+  forall {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u1 u3, max u1 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (fun (_x : Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) => Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, max u3 u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.dualMap.{u3, u1, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) M' (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (Submodule.subtype.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))))) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u3, max u3 u2} R (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.range.{u3, u3, max u3 u1, max u3 u2, max (max u3 u2) u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, max u1 u3, max u2 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u3, u3, max u3 u1, max u3 u2} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.dualMap.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)))
 Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjectiveₓ'. -/
 -- Note, this can be specialized to the case where `R` is an injective `R`-module, or when
 -- `f.coker` is a projective `R`-module.
@@ -1915,7 +1915,7 @@ theorem dualPairing_nondegenerate : (dualPairing K V₁).Nondegenerate :=
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) -> (Function.Surjective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f)))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f)) -> (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f)))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f)) -> (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f)))
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_surjective_of_injective LinearMap.dualMap_surjective_of_injectiveₓ'. -/
 theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function.Injective f) :
     Function.Surjective f.dualMap := by
@@ -1941,7 +1941,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker (f : V₁ →ₗ[K] V₂) :
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Surjective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Injective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Injective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Injective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_surjective_iff LinearMap.dualMap_surjective_iffₓ'. -/
 /-- For vector spaces, `f.dual_map` is surjective if and only if `f` is injective -/
 @[simp]
@@ -2092,7 +2092,7 @@ theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Injective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Surjective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Surjective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Surjective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iffₓ'. -/
 /-- `f.dual_map` is injective if and only if `f` is surjective -/
 @[simp]
@@ -2113,7 +2113,7 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Bijective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Bijective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Bijective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Bijective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Bijective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Bijective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_bijective_iff LinearMap.dualMap_bijective_iffₓ'. -/
 /-- `f.dual_map` is bijective if and only if `f` is -/
 @[simp]
@@ -2170,7 +2170,7 @@ variable {R M N}
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_5 : CommSemiring.{u1} R] [_inst_6 : AddCommMonoid.{u2} M] [_inst_7 : AddCommMonoid.{u3} N] [_inst_8 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6] [_inst_9 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7] (f : Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (g : Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (m : M) (n : N), Eq.{succ u1} R (coeFn.{max (succ (max u2 u3)) (succ u1), max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (fun (_x : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) => (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (coeFn.{max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1))} (LinearMap.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5))) (fun (_x : LinearMap.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5))) => (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) -> (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9))) (LinearMap.hasCoeToFun.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.dualDistrib.{u1, u2, u3} R M N _inst_5 _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.tmul.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5)) f g)) (TensorProduct.tmul.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (fun (_x : Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_5 _inst_6 _inst_8) f m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (fun (_x : Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) => N -> R) (Module.Dual.hasCoeToFun.{u1, u3} R N _inst_5 _inst_7 _inst_9) g n))
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_5 : CommSemiring.{u3} R] [_inst_6 : AddCommMonoid.{u2} M] [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6] [_inst_9 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7] (f : Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (g : Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (m : M) (n : N), Eq.{succ u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => R) (TensorProduct.tmul.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.tmul.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) f g)) (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => R) _x) (Module.Dual.instFunLikeDual.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u3, u3, max (max u1 u3) u2 u3, max (max u1 u2) u3} R R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.addCommMonoid.{u3, u3, max u2 u1, u3} R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u2 u1, u3} R R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (fun (_x : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max (max u3 u2) u1, max (max u3 u2) u1} R R (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.addCommMonoid.{u3, u3, max u2 u1, u3} R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u2 u1, u3} R R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.dualDistrib.{u3, u2, u1} R M N _inst_5 _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.tmul.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) f g)) (TensorProduct.tmul.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (HMul.hMul.{u3, u3, u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : N) => R) n) ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (instHMul.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) _inst_5))))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u3, u2} R M _inst_5 _inst_6 _inst_8) f m) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) N (fun (_x : N) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : N) => R) _x) (Module.Dual.instFunLikeDual.{u3, u1} R N _inst_5 _inst_7 _inst_9) g n))
+  forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_5 : CommSemiring.{u3} R] [_inst_6 : AddCommMonoid.{u2} M] [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6] [_inst_9 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7] (f : Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (g : Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (m : M) (n : N), Eq.{succ u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => R) (TensorProduct.tmul.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.tmul.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) f g)) (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => R) _x) (Module.Dual.instFunLikeDual.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u3, u3, max (max u1 u3) u2 u3, max (max u1 u2) u3} R R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.addCommMonoid.{u3, u3, max u2 u1, u3} R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u2 u1, u3} R R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (fun (_x : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max (max u3 u2) u1, max (max u3 u2) u1} R R (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.addCommMonoid.{u3, u3, max u2 u1, u3} R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u2 u1, u3} R R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.dualDistrib.{u3, u2, u1} R M N _inst_5 _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.tmul.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) f g)) (TensorProduct.tmul.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (HMul.hMul.{u3, u3, u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : N) => R) n) ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (instHMul.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) _inst_5))))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u3, u2} R M _inst_5 _inst_6 _inst_8) f m) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) N (fun (_x : N) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : N) => R) _x) (Module.Dual.instFunLikeDual.{u3, u1} R N _inst_5 _inst_7 _inst_9) g n))
 Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_apply TensorProduct.dualDistrib_applyₓ'. -/
 @[simp]
 theorem dualDistrib_apply (f : Dual R M) (g : Dual R N) (m : M) (n : N) :
@@ -2206,7 +2206,7 @@ noncomputable def dualDistribInvOfBasis (b : Basis ι R M) (c : Basis κ R N) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {ι : Type.{u4}} {κ : Type.{u5}} [_inst_1 : DecidableEq.{succ u4} ι] [_inst_2 : DecidableEq.{succ u5} κ] [_inst_3 : Fintype.{u4} ι] [_inst_4 : Fintype.{u5} κ] [_inst_5 : CommRing.{u1} R] [_inst_6 : AddCommGroup.{u2} M] [_inst_7 : AddCommGroup.{u3} N] [_inst_8 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6)] [_inst_9 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7)] (b : Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (c : Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (f : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)), Eq.{succ (max (max u2 u1) u3 u1)} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (coeFn.{max (succ (max (max u2 u3) u1)) (succ (max (max u2 u1) u3 u1)), max (succ (max (max u2 u3) u1)) (succ (max (max u2 u1) u3 u1))} (LinearMap.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) (fun (_x : LinearMap.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) => (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) -> (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) (LinearMap.hasCoeToFun.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (TensorProduct.dualDistribInvOfBasis.{u1, u2, u3, u4, u5} R M N ι κ (fun (a : ι) (b : ι) => _inst_1 a b) (fun (a : κ) (b : κ) => _inst_2 a b) _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 b c) f) (Finset.sum.{max (max u2 u1) u3 u1, u4} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) ι (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Finset.univ.{u4} ι _inst_3) (fun (i : ι) => Finset.sum.{max (max u2 u1) u3 u1, u5} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) κ (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Finset.univ.{u5} κ _inst_4) (fun (j : κ) => SMul.smul.{u1, max (max u2 u1) u3 u1} R (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (TensorProduct.hasSmul.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (coeFn.{max (succ (max u2 u3)) (succ u1), max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (fun (_x : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) => (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) f (TensorProduct.tmul.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9 (coeFn.{max (succ u4) (succ u1) (succ u2), max (succ u4) (succ u2)} (Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (fun (_x : Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) => ι -> M) (FunLike.hasCoeToFun.{max (succ u4) (succ u1) (succ u2), succ u4, succ u2} (Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) ι (fun (_x : ι) => M) (Basis.funLike.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8)) b i) (coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (fun (_x : Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) => κ -> N) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) κ (fun (_x : κ) => N) (Basis.funLike.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9)) c j))) (TensorProduct.tmul.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)) (coeFn.{max (succ u4) (succ u1) (succ (max u2 u1)), max (succ u4) (succ (max u2 u1))} (Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) (fun (_x : Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8)) (FunLike.hasCoeToFun.{max (succ u4) (succ u1) (succ (max u2 u1)), succ u4, succ (max u2 u1)} (Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Basis.funLike.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5)))) (Basis.dualBasis.{u1, u2, u4} R M ι _inst_5 _inst_6 _inst_8 (fun (a : ι) (b : ι) => _inst_1 a b) b (Finite.of_fintype.{u4} ι _inst_3)) i) (coeFn.{max (succ u5) (succ u1) (succ (max u3 u1)), max (succ u5) (succ (max u3 u1))} (Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) (fun (_x : Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) => κ -> (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9)) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ (max u3 u1)), succ u5, succ (max u3 u1)} (Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) κ (fun (_x : κ) => Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Basis.funLike.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5)))) (Basis.dualBasis.{u1, u3, u5} R N κ _inst_5 _inst_7 _inst_9 (fun (a : κ) (b : κ) => _inst_2 a b) c (Finite.of_fintype.{u5} κ _inst_4)) j)))))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {ι : Type.{u5}} {κ : Type.{u2}} [_inst_1 : DecidableEq.{succ u5} ι] [_inst_2 : DecidableEq.{succ u2} κ] [_inst_3 : Fintype.{u5} ι] [_inst_4 : Fintype.{u2} κ] [_inst_5 : CommRing.{u4} R] [_inst_6 : AddCommGroup.{u3} M] [_inst_7 : AddCommGroup.{u1} N] [_inst_8 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6)] [_inst_9 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7)] (b : Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (c : Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (f : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)), Eq.{max (max (succ u4) (succ u3)) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (max (succ u4) (succ u3)) (succ u1), max (max (succ u4) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max (max u1 u3) u4, max (max u1 u4) u3 u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u4} R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u4} R R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))))) (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (fun (_x : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max (max u4 u3) u1, max (max u4 u3) u1} R R (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u4} R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u4} R R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.dualDistribInvOfBasis.{u4, u3, u1, u5, u2} R M N ι κ (fun (a : ι) (b : ι) => _inst_1 a b) (fun (a : κ) (b : κ) => _inst_2 a b) _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 b c) f) (Finset.sum.{max (max u4 u3) u1, u5} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) ι (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Finset.univ.{u5} ι _inst_3) (fun (i : ι) => Finset.sum.{max (max u4 u3) u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) κ (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Finset.univ.{u2} κ _inst_4) (fun (j : κ) => HSMul.hSMul.{u4, max (max u4 u1) u4 u3, max (max u4 u3) u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5)))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) (instHSMul.{u4, max (max u4 u3) u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5)))))) (TensorProduct.instSMulTensorProduct.{u4, max u4 u3, max u4 u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u4} (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (fun (_x : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) _x) (Module.Dual.instFunLikeDual.{u4, max u3 u1} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) f (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (_x : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) _x) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.tmul.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, max (succ u4) (succ u3)} (Basis.{u5, u4, max u3 u4} ι R (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) _x) (Basis.funLike.{u5, u4, max u4 u3} ι R (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Basis.dualBasis.{u4, u3, u5} R M ι _inst_5 _inst_6 _inst_8 (fun (a : ι) (b : ι) => _inst_1 a b) b (Finite.of_fintype.{u5} ι _inst_3)) i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, max (succ u4) (succ u1)} (Basis.{u2, u4, max u1 u4} κ R (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) κ (fun (_x : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) _x) (Basis.funLike.{u2, u4, max u4 u1} κ R (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Basis.dualBasis.{u4, u1, u2} R N κ _inst_5 _inst_7 _inst_9 (fun (a : κ) (b : κ) => _inst_2 a b) c (Finite.of_fintype.{u2} κ _inst_4)) j)))))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {ι : Type.{u5}} {κ : Type.{u2}} [_inst_1 : DecidableEq.{succ u5} ι] [_inst_2 : DecidableEq.{succ u2} κ] [_inst_3 : Fintype.{u5} ι] [_inst_4 : Fintype.{u2} κ] [_inst_5 : CommRing.{u4} R] [_inst_6 : AddCommGroup.{u3} M] [_inst_7 : AddCommGroup.{u1} N] [_inst_8 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6)] [_inst_9 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7)] (b : Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (c : Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (f : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)), Eq.{max (max (succ u4) (succ u3)) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (max (succ u4) (succ u3)) (succ u1), max (max (succ u4) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max (max u1 u3) u4, max (max u1 u4) u3 u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u4} R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u4} R R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))))) (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (fun (_x : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max (max u4 u3) u1, max (max u4 u3) u1} R R (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u4} R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u4} R R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.dualDistribInvOfBasis.{u4, u3, u1, u5, u2} R M N ι κ (fun (a : ι) (b : ι) => _inst_1 a b) (fun (a : κ) (b : κ) => _inst_2 a b) _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 b c) f) (Finset.sum.{max (max u4 u3) u1, u5} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) ι (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Finset.univ.{u5} ι _inst_3) (fun (i : ι) => Finset.sum.{max (max u4 u3) u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) κ (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Finset.univ.{u2} κ _inst_4) (fun (j : κ) => HSMul.hSMul.{u4, max (max u4 u1) u4 u3, max (max u4 u3) u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5)))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) (instHSMul.{u4, max (max u4 u3) u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5)))))) (TensorProduct.instSMulTensorProduct.{u4, max u4 u3, max u4 u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u4} (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (fun (_x : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) _x) (Module.Dual.instFunLikeDual.{u4, max u3 u1} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) f (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (_x : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) _x) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.tmul.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, max (succ u4) (succ u3)} (Basis.{u5, u4, max u3 u4} ι R (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) _x) (Basis.funLike.{u5, u4, max u4 u3} ι R (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Basis.dualBasis.{u4, u3, u5} R M ι _inst_5 _inst_6 _inst_8 (fun (a : ι) (b : ι) => _inst_1 a b) b (Finite.of_fintype.{u5} ι _inst_3)) i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, max (succ u4) (succ u1)} (Basis.{u2, u4, max u1 u4} κ R (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) κ (fun (_x : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) _x) (Basis.funLike.{u2, u4, max u4 u1} κ R (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Basis.dualBasis.{u4, u1, u2} R N κ _inst_5 _inst_7 _inst_9 (fun (a : κ) (b : κ) => _inst_2 a b) c (Finite.of_fintype.{u2} κ _inst_4)) j)))))
 Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_inv_of_basis_apply TensorProduct.dualDistribInvOfBasis_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
 
 ! This file was ported from Lean 3 source module linear_algebra.dual
-! leanprover-community/mathlib commit b1c017582e9f18d8494e5c18602a8cb4a6f843ac
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.LinearAlgebra.FreeModule.Finite.Basic
 /-!
 # Dual vector spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The dual space of an $R$-module $M$ is the $R$-module of $R$-linear maps $M \to R$.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/1b0a28e1c93409dbf6d69526863cd9984ef652ce

@@ -100,18 +100,28 @@ variable (R : Type _) (M : Type _)
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M]
 
+#print Module.Dual /-
 /-- The dual space of an R-module M is the R-module of linear maps `M → R`. -/
 @[reducible]
 def Dual :=
   M →ₗ[R] R
 #align module.dual Module.Dual
+-/
 
+#print Module.dualPairing /-
 /-- The canonical pairing of a vector space and its algebraic dual. -/
 def dualPairing (R M) [CommSemiring R] [AddCommMonoid M] [Module R M] :
     Module.Dual R M →ₗ[R] M →ₗ[R] R :=
   LinearMap.id
 #align module.dual_pairing Module.dualPairing
+-/
 
+/- warning: module.dual_pairing_apply -> Module.dualPairing_apply is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => M -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualPairing._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) => M -> R) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) v x)
+but is expected to have type
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) v) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) v x)
+Case conversion may be inaccurate. Consider using '#align module.dual_pairing_apply Module.dualPairing_applyₓ'. -/
 @[simp]
 theorem dualPairing_apply (v x) : dualPairing R M v x = v x :=
   rfl
@@ -125,12 +135,20 @@ instance : Inhabited (Dual R M) :=
 instance : CoeFun (Dual R M) fun _ => M → R :=
   ⟨LinearMap.toFun⟩
 
+#print Module.Dual.eval /-
 /-- Maps a module M to the dual of the dual of M. See `module.erange_coe` and
 `module.eval_equiv`. -/
 def eval : M →ₗ[R] Dual R (Dual R M) :=
   LinearMap.flip LinearMap.id
 #align module.dual.eval Module.Dual.eval
+-/
 
+/- warning: module.dual.eval_apply -> Module.Dual.eval_apply is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : M) (a : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (fun (_x : Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1))) => M -> (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_1.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.eval._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.eval.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) a) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) a v)
+but is expected to have type
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (v : M) (a : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => R) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) v) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => R) _x) (Module.Dual.instFunLikeDual.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u1 u2, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_1 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, max u1 u2, u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, u1} R R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.eval.{u1, u2} R M _inst_1 _inst_2 _inst_3) v) a) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) a v)
+Case conversion may be inaccurate. Consider using '#align module.dual.eval_apply Module.Dual.eval_applyₓ'. -/
 @[simp]
 theorem eval_apply (v : M) (a : Dual R M) : eval R M v a = a v :=
   rfl
@@ -138,22 +156,32 @@ theorem eval_apply (v : M) (a : Dual R M) : eval R M v a = a v :=
 
 variable {R M} {M' : Type _} [AddCommMonoid M'] [Module R M']
 
+#print Module.Dual.transpose /-
 /-- The transposition of linear maps, as a linear map from `M →ₗ[R] M'` to
 `dual R M' →ₗ[R] dual R M`. -/
 def transpose : (M →ₗ[R] M') →ₗ[R] Dual R M' →ₗ[R] Dual R M :=
   (LinearMap.llcomp R M M' R).flip
 #align module.dual.transpose Module.Dual.transpose
+-/
 
+/- warning: module.dual.transpose_apply -> Module.Dual.transpose_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {M' : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (u : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (l : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ (max u2 u3)) (succ (max (max u3 u1) u2 u1)), max (succ (max u2 u3)) (succ (max (max u3 u1) u2 u1))} (LinearMap.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3))) => (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) -> (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u3, max (max u3 u1) u2 u1} R R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (Module.Dual.transpose._proof_3.{u1, u3} R _inst_1 M' _inst_4 _inst_5)) (LinearMap.module.{u1, u1, u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.transpose._proof_2.{u1} R _inst_1)) (Module.Dual.transpose._proof_4.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.transpose.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) u) l) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) l u)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {M' : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (u : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (l : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) l) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) u) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u1, u1, max u3 u2, max (max u2 u1) u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (smulCommClass_self.{u1, u3} R M' (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u3, max u1 u2} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u1, u2, u1} R R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) => LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u3 u2, max (max u1 u3) u2} R R (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M M' _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u3} R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u3} R R R M M' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_5 (smulCommClass_self.{u1, u3} R M' (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u3} R M' (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} M' (AddCommMonoid.toAddMonoid.{u3} M' _inst_4)) (Module.toMulActionWithZero.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u3, max u1 u2} R R R (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instSMulCommClassLinearMapInstSMulLinearMapInstSMulLinearMap.{u1, u1, u1, u1, u2, u1} R R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.Dual.transpose.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) u) l) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) l u)
+Case conversion may be inaccurate. Consider using '#align module.dual.transpose_apply Module.Dual.transpose_applyₓ'. -/
 theorem transpose_apply (u : M →ₗ[R] M') (l : Dual R M') : transpose u l = l.comp u :=
   rfl
 #align module.dual.transpose_apply Module.Dual.transpose_apply
 
 variable {M'' : Type _} [AddCommMonoid M''] [Module R M'']
 
+#print Module.Dual.transpose_comp /-
 theorem transpose_comp (u : M' →ₗ[R] M'') (v : M →ₗ[R] M') :
     transpose (u.comp v) = (transpose v).comp (transpose u) :=
   rfl
 #align module.dual.transpose_comp Module.Dual.transpose_comp
+-/
 
 end Dual
 
@@ -161,12 +189,24 @@ section Prod
 
 variable (M' : Type _) [AddCommMonoid M'] [Module R M']
 
+/- warning: module.dual_prod_dual_equiv_dual -> Module.dualProdDualEquivDual is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4], LinearEquiv.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1))
+but is expected to have type
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4], LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align module.dual_prod_dual_equiv_dual Module.dualProdDualEquivDualₓ'. -/
 /-- Taking duals distributes over products. -/
 @[simps]
 def dualProdDualEquivDual : (Module.Dual R M × Module.Dual R M') ≃ₗ[R] Module.Dual R (M × M') :=
   LinearMap.coprodEquiv R
 #align module.dual_prod_dual_equiv_dual Module.dualProdDualEquivDual
 
+/- warning: module.dual_prod_dual_equiv_dual_apply -> Module.dualProdDualEquivDual_apply is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ψ : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (coeFn.{max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1))} (LinearEquiv.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1))) => (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) -> (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5))) (LinearEquiv.hasCoeToFun.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u2 u1, max u3 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_3.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_4.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.dualProdDualEquivDual._proof_5.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.dualProdDualEquivDual._proof_1.{u1} R _inst_1) (Module.dualProdDualEquivDual._proof_2.{u1} R _inst_1)) (Module.dualProdDualEquivDual.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) (Prod.mk.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (LinearMap.coprod.{u1, u2, u3, u1} R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ ψ)
+but is expected to have type
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (M' : Type.{u3}) [_inst_4 : AddCommMonoid.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ψ : Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5), Eq.{max (max (succ u1) (succ u2)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.mk.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (fun (_x : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) => Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max (max u1 u2) u3, max (max u1 u2) u3} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (SMulZeroClass.toSMul.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddMonoid.toZero.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddMonoid.toZero.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddMonoid.toAddZeroClass.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max (max u1 u2) u3, max (max u1 u2) u3} (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max (max u1 u2) u3} (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max (max u1 u2) u3} R (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max (max u1 u2) u3, max (max u1 u2) u3, max (max u1 u2) u3} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (LinearEquiv.{u1, u1, max (max u3 u1) u2 u1, max (max u3 u2) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max (max u1 u2) u3, max (max u1 u2) u3} R R (Prod.{max u2 u1, max u3 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5)) (Module.Dual.{u1, max u3 u2} R (Prod.{u2, u3} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, max u1 u2, max u1 u3} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (Prod.{u2, u3} M M') R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M M' _inst_2 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.module.{u1, u2, u3} R M M' (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.dualProdDualEquivDual.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 M' _inst_4 _inst_5) (Prod.mk.{max u1 u2, max u1 u3} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u3} R M' _inst_1 _inst_4 _inst_5) φ ψ)) (LinearMap.coprod.{u1, u2, u3, u1} R M M' R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) φ ψ)
+Case conversion may be inaccurate. Consider using '#align module.dual_prod_dual_equiv_dual_apply Module.dualProdDualEquivDual_applyₓ'. -/
 @[simp]
 theorem dualProdDualEquivDual_apply (φ : Module.Dual R M) (ψ : Module.Dual R M') :
     dualProdDualEquivDual R M M' (φ, ψ) = φ.coprod ψ :=
@@ -185,38 +225,68 @@ variable {R : Type _} [CommSemiring R] {M₁ : Type _} {M₂ : Type _}
 
 variable [AddCommMonoid M₁] [Module R M₁] [AddCommMonoid M₂] [Module R M₂]
 
+#print LinearMap.dualMap /-
 /-- Given a linear map `f : M₁ →ₗ[R] M₂`, `f.dual_map` is the linear map between the dual of
 `M₂` and `M₁` such that it maps the functional `φ` to `φ ∘ f`. -/
 def LinearMap.dualMap (f : M₁ →ₗ[R] M₂) : Dual R M₂ →ₗ[R] Dual R M₁ :=
   Module.Dual.transpose f
 #align linear_map.dual_map LinearMap.dualMap
+-/
 
+#print LinearMap.dualMap_def /-
 theorem LinearMap.dualMap_def (f : M₁ →ₗ[R] M₂) : f.dualMap = Module.Dual.transpose f :=
   rfl
 #align linear_map.dual_map_def LinearMap.dualMap_def
+-/
 
+/- warning: linear_map.dual_map_apply' -> LinearMap.dualMap_apply' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M₁ M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) (LinearMap.comp.{u1, u1, u1, u2, u3, u1} R R R M₁ M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f)
+Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_apply' LinearMap.dualMap_apply'ₓ'. -/
 theorem LinearMap.dualMap_apply' (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) : f.dualMap g = g.comp f :=
   rfl
 #align linear_map.dual_map_apply' LinearMap.dualMap_apply'
 
+/- warning: linear_map.dual_map_apply -> LinearMap.dualMap_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) => M₁ -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => M₂ -> R) (Module.Dual.hasCoeToFun.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₂) => R) _x) (Module.Dual.instFunLikeDual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f x))
+Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_apply LinearMap.dualMap_applyₓ'. -/
 @[simp]
 theorem LinearMap.dualMap_apply (f : M₁ →ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
     f.dualMap g x = g (f x) :=
   rfl
 #align linear_map.dual_map_apply LinearMap.dualMap_apply
 
+#print LinearMap.dualMap_id /-
 @[simp]
 theorem LinearMap.dualMap_id : (LinearMap.id : M₁ →ₗ[R] M₁).dualMap = LinearMap.id :=
   by
   ext
   rfl
 #align linear_map.dual_map_id LinearMap.dualMap_id
+-/
 
+/- warning: linear_map.dual_map_comp_dual_map -> LinearMap.dualMap_comp_dualMap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {M₃ : Type.{u4}} [_inst_6 : AddCommGroup.{u4} M₃] [_inst_7 : Module.{u1, u4} R M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6)] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₂ M₃ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_5 _inst_7), Eq.{max (succ (max u4 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u4 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u4, u1} R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u4, u1} R R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (LinearMap.comp.{u1, u1, u1, max u4 u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u4, u1} R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u4, u1} R R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) (LinearMap.dualMap.{u1, u3, u4} R _inst_1 M₂ M₃ _inst_4 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7 g)) (LinearMap.dualMap.{u1, u2, u4} R _inst_1 M₁ M₃ _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7 (LinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R M₁ M₂ M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_3 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) g f))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M₁ : Type.{u3}} {M₂ : Type.{u4}} [_inst_2 : AddCommMonoid.{u3} M₁] [_inst_3 : Module.{u2, u3} R M₁ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u4} M₂] [_inst_5 : Module.{u2, u4} R M₂ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] {M₃ : Type.{u1}} [_inst_6 : AddCommGroup.{u1} M₃] [_inst_7 : Module.{u2, u1} R M₃ (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6)] (f : LinearMap.{u2, u2, u3, u4} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : LinearMap.{u2, u2, u4, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M₂ M₃ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_5 _inst_7), Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearMap.{u2, u2, max u2 u1, max u2 u3} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7) (Module.Dual.{u2, u3} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (LinearMap.comp.{u2, u2, u2, max u2 u1, max u2 u4, max u2 u3} R R R (Module.Dual.{u2, u1} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7) (Module.Dual.{u2, u4} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u2, u3} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u4, u2} R R M₂ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u4, u2} R R R M₂ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.dualMap.{u2, u3, u4} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) (LinearMap.dualMap.{u2, u4, u1} R _inst_1 M₂ M₃ _inst_4 _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7 g)) (LinearMap.dualMap.{u2, u3, u1} R _inst_1 M₁ M₃ _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7 (LinearMap.comp.{u2, u2, u2, u3, u4, u1} R R R M₁ M₂ M₃ (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_3 _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) g f))
+Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_comp_dual_map LinearMap.dualMap_comp_dualMapₓ'. -/
 theorem LinearMap.dualMap_comp_dualMap {M₃ : Type _} [AddCommGroup M₃] [Module R M₃]
     (f : M₁ →ₗ[R] M₂) (g : M₂ →ₗ[R] M₃) : f.dualMap.comp g.dualMap = (g.comp f).dualMap :=
   rfl
 #align linear_map.dual_map_comp_dual_map LinearMap.dualMap_comp_dualMap
 
+/- warning: linear_map.dual_map_injective_of_surjective -> LinearMap.dualMap_injective_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5}, (Function.Surjective.{succ u2, succ u3} M₁ M₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5}, (Function.Surjective.{succ u2, succ u3} M₁ M₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M₁) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)))
+Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_injective_of_surjective LinearMap.dualMap_injective_of_surjectiveₓ'. -/
 /-- If a linear map is surjective, then its dual is injective. -/
 theorem LinearMap.dualMap_injective_of_surjective {f : M₁ →ₗ[R] M₂} (hf : Function.Surjective f) :
     Function.Injective f.dualMap := by
@@ -226,6 +296,7 @@ theorem LinearMap.dualMap_injective_of_surjective {f : M₁ →ₗ[R] M₂} (hf
   exact congr_arg (fun g : Module.Dual R M₁ => g y) h
 #align linear_map.dual_map_injective_of_surjective LinearMap.dualMap_injective_of_surjective
 
+#print LinearEquiv.dualMap /-
 /-- The `linear_equiv` version of `linear_map.dual_map`. -/
 def LinearEquiv.dualMap (f : M₁ ≃ₗ[R] M₂) : Dual R M₂ ≃ₗ[R] Dual R M₁ :=
   { f.toLinearMap.dualMap with
@@ -239,13 +310,21 @@ def LinearEquiv.dualMap (f : M₁ ≃ₗ[R] M₂) : Dual R M₂ ≃ₗ[R] Dual R
       simp only [LinearMap.dualMap_apply, LinearEquiv.coe_toLinearMap, LinearMap.toFun_eq_coe,
         LinearEquiv.symm_apply_apply] }
 #align linear_equiv.dual_map LinearEquiv.dualMap
+-/
 
+/- warning: linear_equiv.dual_map_apply -> LinearEquiv.dualMap_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) => M₁ -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1))) => (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) -> (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3)) (LinearEquiv.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1)) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => M₂ -> R) (Module.Dual.hasCoeToFun.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) => M₁ -> M₂) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (x : M₁), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) g) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₁) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (fun (_x : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) => Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u3, max u1 u2} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddMonoid.toZero.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddMonoid.toAddZeroClass.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u3, max u1 u2} (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearEquiv.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f) g) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) M₂ (fun (_x : M₂) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M₂) => R) _x) (Module.Dual.instFunLikeDual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) M₁ (fun (_x : M₁) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M₁) => M₂) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) R M₁ M₂ (SMulZeroClass.toSMul.{u1, u2} R M₁ (AddMonoid.toZero.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M₁ (AddMonoid.toAddZeroClass.{u2} M₁ (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M₁ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2) (Module.toDistribMulAction.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, u3} R M₂ (AddMonoid.toZero.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4)) (DistribSMul.toSMulZeroClass.{u1, u3} R M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4)) (DistribMulAction.toDistribSMul.{u1, u3} R M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4) (Module.toDistribMulAction.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) R M₁ M₂ (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M₁ _inst_2) (AddCommMonoid.toAddMonoid.{u3} M₂ _inst_4) (Module.toDistribMulAction.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_5) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} R M₁ M₂ (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u3, max u2 u3} R R M₁ M₂ (LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) f x))
+Case conversion may be inaccurate. Consider using '#align linear_equiv.dual_map_apply LinearEquiv.dualMap_applyₓ'. -/
 @[simp]
 theorem LinearEquiv.dualMap_apply (f : M₁ ≃ₗ[R] M₂) (g : Dual R M₂) (x : M₁) :
     f.dualMap g x = g (f x) :=
   rfl
 #align linear_equiv.dual_map_apply LinearEquiv.dualMap_apply
 
+#print LinearEquiv.dualMap_refl /-
 @[simp]
 theorem LinearEquiv.dualMap_refl :
     (LinearEquiv.refl R M₁).dualMap = LinearEquiv.refl R (Dual R M₁) :=
@@ -253,13 +332,22 @@ theorem LinearEquiv.dualMap_refl :
   ext
   rfl
 #align linear_equiv.dual_map_refl LinearEquiv.dualMap_refl
+-/
 
+#print LinearEquiv.dualMap_symm /-
 @[simp]
 theorem LinearEquiv.dualMap_symm {f : M₁ ≃ₗ[R] M₂} :
     (LinearEquiv.dualMap f).symm = LinearEquiv.dualMap f.symm :=
   rfl
 #align linear_equiv.dual_map_symm LinearEquiv.dualMap_symm
+-/
 
+/- warning: linear_equiv.dual_map_trans -> LinearEquiv.dualMap_trans is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {M₃ : Type.{u4}} [_inst_6 : AddCommGroup.{u4} M₃] [_inst_7 : Module.{u1, u4} R M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6)] (f : LinearEquiv.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : LinearEquiv.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M₂ M₃ _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_5 _inst_7), Eq.{max (succ (max u4 u1)) (succ (max u2 u1))} (LinearEquiv.{u1, u1, max u4 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (Module.Dual.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u4, u1} R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u4, u1} R R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1))) (LinearEquiv.trans.{u1, u1, u1, max u4 u1, max u3 u1, max u2 u1} R R R (Module.Dual.{u1, u4} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u4, u1} R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u4, u1} R R R M₃ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_7 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_5.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_6.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_3.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (LinearEquiv.dualMap._proof_4.{u1} R _inst_1) (LinearEquiv.dualMap.{u1, u3, u4} R _inst_1 M₂ M₃ _inst_4 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7 g) (LinearEquiv.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)) (LinearEquiv.dualMap.{u1, u2, u4} R _inst_1 M₁ M₃ _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_7 (LinearEquiv.trans.{u1, u1, u1, u2, u3, u4} R R R M₁ M₂ M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 (AddCommGroup.toAddCommMonoid.{u4} M₃ _inst_6) _inst_3 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_1.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.dualMap._proof_2.{u1} R _inst_1) f g))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {M₁ : Type.{u3}} {M₂ : Type.{u4}} [_inst_2 : AddCommMonoid.{u3} M₁] [_inst_3 : Module.{u2, u3} R M₁ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u4} M₂] [_inst_5 : Module.{u2, u4} R M₂ (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] {M₃ : Type.{u1}} [_inst_6 : AddCommGroup.{u1} M₃] [_inst_7 : Module.{u2, u1} R M₃ (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6)] (f : LinearEquiv.{u2, u2, u3, u4} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (g : LinearEquiv.{u2, u2, u4, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M₂ M₃ _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_5 _inst_7), Eq.{max (max (succ u2) (succ u3)) (succ u1)} (LinearEquiv.{u2, u2, max u2 u1, max u2 u3} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Module.Dual.{u2, u1} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7) (Module.Dual.{u2, u3} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (LinearEquiv.trans.{u2, u2, u2, max u2 u1, max u2 u4, max u2 u3} R R R (Module.Dual.{u2, u1} R M₃ _inst_1 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7) (Module.Dual.{u2, u4} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u2, u3} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u4, u2} R R M₂ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M₃ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_7 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u4, u2} R R R M₂ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M₁ R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.dualMap.{u2, u4, u1} R _inst_1 M₂ M₃ _inst_4 _inst_5 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7 g) (LinearEquiv.dualMap.{u2, u3, u4} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)) (LinearEquiv.dualMap.{u2, u3, u1} R _inst_1 M₁ M₃ _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_7 (LinearEquiv.trans.{u2, u2, u2, u3, u4, u1} R R R M₁ M₂ M₃ (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_4 (AddCommGroup.toAddCommMonoid.{u1} M₃ _inst_6) _inst_3 _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHomCompTriple.ids.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) f g))
+Case conversion may be inaccurate. Consider using '#align linear_equiv.dual_map_trans LinearEquiv.dualMap_transₓ'. -/
 theorem LinearEquiv.dualMap_trans {M₃ : Type _} [AddCommGroup M₃] [Module R M₃] (f : M₁ ≃ₗ[R] M₂)
     (g : M₂ ≃ₗ[R] M₃) : g.dualMap.trans f.dualMap = (f.trans g).dualMap :=
   rfl
@@ -283,18 +371,32 @@ variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
 
 variable (b : Basis ι R M)
 
+#print Basis.toDual /-
 /-- The linear map from a vector space equipped with basis to its dual vector space,
 taking basis elements to corresponding dual basis elements. -/
 def toDual : M →ₗ[R] Module.Dual R M :=
   b.constr ℕ fun v => b.constr ℕ fun w => if w = v then (1 : R) else 0
 #align basis.to_dual Basis.toDual
+-/
 
+/- warning: basis.to_dual_apply -> Basis.toDual_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (j : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b j)) (ite.{succ u1} R (Eq.{succ u3} ι i j) (_inst_4 i j) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (ite.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (Eq.{succ u3} ι i j) (_inst_4 i j) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b j)) _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply Basis.toDual_applyₓ'. -/
 theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0 :=
   by
   erw [constr_basis b, constr_basis b]
   ac_rfl
 #align basis.to_dual_apply Basis.toDual_apply
 
+/- warning: basis.to_dual_total_left -> Basis.toDual_total_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b)) f)) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (a : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) f i)
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_total_left Basis.toDual_total_leftₓ'. -/
 @[simp]
 theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total ι M R b f) (b i) = f i :=
   by
@@ -306,6 +408,12 @@ theorem toDual_total_left (f : ι →₀ R) (i : ι) : b.toDual (Finsupp.total 
   · rw [finsupp.not_mem_support_iff.mp h]
 #align basis.to_dual_total_left Basis.toDual_total_left
 
+/- warning: basis.to_dual_total_right -> Basis.toDual_total_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b)) f)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) f i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (a : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) a) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (LinearMap.{u1, u1, max u1 u3, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.total.{u3, u2, u1} ι M R (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b)) f)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))) f i)
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_total_right Basis.toDual_total_rightₓ'. -/
 @[simp]
 theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.total ι M R b f) = f i :=
   by
@@ -316,37 +424,81 @@ theorem toDual_total_right (f : ι →₀ R) (i : ι) : b.toDual (b i) (Finsupp.
   · rw [finsupp.not_mem_support_iff.mp h]
 #align basis.to_dual_total_right Basis.toDual_total_right
 
+/- warning: basis.to_dual_apply_left -> Basis.toDual_apply_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply_left Basis.toDual_apply_leftₓ'. -/
 theorem toDual_apply_left (m : M) (i : ι) : b.toDual m (b i) = b.repr m i := by
   rw [← b.to_dual_total_left, b.total_repr]
 #align basis.to_dual_apply_left Basis.toDual_apply_left
 
+/- warning: basis.to_dual_apply_right -> Basis.toDual_apply_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (m : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι) (m : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_apply_right Basis.toDual_apply_rightₓ'. -/
 theorem toDual_apply_right (i : ι) (m : M) : b.toDual (b i) m = b.repr m i := by
   rw [← b.to_dual_total_right, b.total_repr]
 #align basis.to_dual_apply_right Basis.toDual_apply_right
 
+/- warning: basis.coe_to_dual_self -> Basis.coe_toDual_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (i : ι), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b i)
+Case conversion may be inaccurate. Consider using '#align basis.coe_to_dual_self Basis.coe_toDual_selfₓ'. -/
 theorem coe_toDual_self (i : ι) : b.toDual (b i) = b.Coord i :=
   by
   ext
   apply to_dual_apply_right
 #align basis.coe_to_dual_self Basis.coe_toDual_self
 
+#print Basis.toDualFlip /-
 /-- `h.to_dual_flip v` is the linear map sending `w` to `h.to_dual w v`. -/
 def toDualFlip (m : M) : M →ₗ[R] R :=
   b.toDual.flip m
 #align basis.to_dual_flip Basis.toDualFlip
+-/
 
+/- warning: basis.to_dual_flip_apply -> Basis.toDualFlip_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m₁ : M) (m₂ : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Basis.toDualFlip.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b m₁) m₂) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m₂) m₁)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m₁ : M) (m₂ : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearMap.{u1, u1, u2, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Basis.toDualFlip.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b m₁) m₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m₂) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m₂) m₁)
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_flip_apply Basis.toDualFlip_applyₓ'. -/
 theorem toDualFlip_apply (m₁ m₂ : M) : b.toDualFlip m₁ m₂ = b.toDual m₂ m₁ :=
   rfl
 #align basis.to_dual_flip_apply Basis.toDualFlip_apply
 
+/- warning: basis.to_dual_eq_repr -> Basis.toDual_eq_repr is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 b) m) i)
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_eq_repr Basis.toDual_eq_reprₓ'. -/
 theorem toDual_eq_repr (m : M) (i : ι) : b.toDual m (b i) = b.repr m i :=
   b.toDual_apply_left m i
 #align basis.to_dual_eq_repr Basis.toDual_eq_repr
 
+/- warning: basis.to_dual_eq_equiv_fun -> Basis.toDual_eq_equivFun is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) [_inst_5 : Fintype.{u3} ι] (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) b i)) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => M -> ι -> R) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.Function.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.equivFun.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 _inst_5 b) m i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) [_inst_5 : Fintype.{u3} ι] (m : M) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => ι -> R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (ι -> R) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (ι -> R) (AddMonoid.toZero.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (ι -> R) (AddMonoid.toAddZeroClass.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R M (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (ι -> R) (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (ι -> R) (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) M (ι -> R) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_3 (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.equivFun.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 _inst_5 b) m i)
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFunₓ'. -/
 theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.equivFun m i := by
   rw [b.equiv_fun_apply, to_dual_eq_repr]
 #align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFun
 
+/- warning: basis.to_dual_inj -> Basis.toDual_inj is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M), (Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Basis.toDual._proof_1.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (OfNat.ofNat.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) 0 (OfNat.mk.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) 0 (Zero.zero.{max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LinearMap.hasZero.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u2} M m (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (m : M), (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Basis.toDual.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) m) (LinearMap.instZeroLinearMap.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) -> (Eq.{succ u2} M m (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_inj Basis.toDual_injₓ'. -/
 theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   by
   rw [← mem_bot R, ← b.repr.ker, mem_ker, LinearEquiv.coe_coe]
@@ -356,10 +508,13 @@ theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   rfl
 #align basis.to_dual_inj Basis.toDual_inj
 
+#print Basis.toDual_ker /-
 theorem toDual_ker : b.toDual.ker = ⊥ :=
   ker_eq_bot'.mpr b.toDual_inj
 #align basis.to_dual_ker Basis.toDual_ker
+-/
 
+#print Basis.toDual_range /-
 theorem toDual_range [Finite ι] : b.toDual.range = ⊤ :=
   by
   cases nonempty_fintype ι
@@ -370,6 +525,7 @@ theorem toDual_range [Finite ι] : b.toDual.range = ⊤ :=
   rw [b.to_dual_eq_repr _ i, repr_total b]
   rfl
 #align basis.to_dual_range Basis.toDual_range
+-/
 
 end CommSemiring
 
@@ -379,6 +535,7 @@ variable [CommSemiring R] [AddCommMonoid M] [Module R M] [Fintype ι]
 
 variable (b : Basis ι R M)
 
+#print Basis.sum_dual_apply_smul_coord /-
 @[simp]
 theorem sum_dual_apply_smul_coord (f : Module.Dual R M) : (∑ x, f (b x) • b.Coord x) = f :=
   by
@@ -386,6 +543,7 @@ theorem sum_dual_apply_smul_coord (f : Module.Dual R M) : (∑ x, f (b x) • b.
   simp_rw [LinearMap.sum_apply, LinearMap.smul_apply, smul_eq_mul, mul_comm (f _), ← smul_eq_mul, ←
     f.map_smul, ← f.map_sum, Basis.coord_apply, Basis.sum_repr]
 #align basis.sum_dual_apply_smul_coord Basis.sum_dual_apply_smul_coord
+-/
 
 end
 
@@ -399,22 +557,38 @@ section Finite
 
 variable [Finite ι]
 
+#print Basis.toDualEquiv /-
 /-- A vector space is linearly equivalent to its dual space. -/
 def toDualEquiv : M ≃ₗ[R] Dual R M :=
   LinearEquiv.ofBijective b.toDual ⟨ker_eq_bot.mp b.toDual_ker, range_eq_top.mp b.toDual_range⟩
 #align basis.to_dual_equiv Basis.toDualEquiv
+-/
 
+/- warning: basis.to_dual_equiv_apply -> Basis.toDualEquiv_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (m : M), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1))) => M -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.toDualEquiv._proof_3.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.toDualEquiv._proof_1.{u1} R _inst_1) (Basis.toDualEquiv._proof_2.{u1} R _inst_1)) (Basis.toDualEquiv.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) m) (coeFn.{max (succ u2) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => M -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.toDual._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Basis.toDual.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (m : M), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, max u1 u2} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, max u1 u2} (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u2, max u1 u2} R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearEquiv.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.toDualEquiv.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u1 u2} R R M (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Basis.toDual.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b) m)
+Case conversion may be inaccurate. Consider using '#align basis.to_dual_equiv_apply Basis.toDualEquiv_applyₓ'. -/
 -- `simps` times out when generating this
 @[simp]
 theorem toDualEquiv_apply (m : M) : b.toDualEquiv m = b.toDual m :=
   rfl
 #align basis.to_dual_equiv_apply Basis.toDualEquiv_apply
 
+#print Basis.dualBasis /-
 /-- Maps a basis for `V` to a basis for the dual space. -/
 def dualBasis : Basis ι R (Dual R M) :=
   b.map b.toDualEquiv
 #align basis.dual_basis Basis.dualBasis
+-/
 
+/- warning: basis.dual_basis_apply_self -> Basis.dualBasis_apply_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (j : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b j)) (ite.{succ u1} R (Eq.{succ u3} ι j i) (_inst_4 j i) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) i) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (ite.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (Eq.{succ u3} ι j i) (_inst_4 j i) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) _inst_1))))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b j)) _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align basis.dual_basis_apply_self Basis.dualBasis_apply_selfₓ'. -/
 -- We use `j = i` to match `basis.repr_self`
 theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1 else 0 :=
   by
@@ -422,6 +596,12 @@ theorem dualBasis_apply_self (i j : ι) : b.dualBasis i (b j) = if j = i then 1
   rw [@eq_comm _ j i]
 #align basis.dual_basis_apply_self Basis.dualBasis_apply_self
 
+/- warning: basis.total_dual_basis -> Basis.total_dualBasis is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5))) f) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) f i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) f) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u3, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5))) f) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f i)
+Case conversion may be inaccurate. Consider using '#align basis.total_dual_basis Basis.total_dualBasisₓ'. -/
 theorem total_dualBasis (f : ι →₀ R) (i : ι) :
     Finsupp.total ι (Dual R M) R b.dualBasis f (b i) = f i :=
   by
@@ -434,21 +614,36 @@ theorem total_dualBasis (f : ι →₀ R) (i : ι) :
     rw [zero_smul]
 #align basis.total_dual_basis Basis.total_dualBasis
 
+/- warning: basis.dual_basis_repr -> Basis.dualBasis_repr is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u3 u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5)) l) i) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u2), max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5)) l) i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i))
+Case conversion may be inaccurate. Consider using '#align basis.dual_basis_repr Basis.dualBasis_reprₓ'. -/
 theorem dualBasis_repr (l : Dual R M) (i : ι) : b.dualBasis.repr l i = l (b i) := by
   rw [← total_dual_basis b, Basis.total_repr b.dual_basis l]
 #align basis.dual_basis_repr Basis.dualBasis_repr
 
+/- warning: basis.dual_basis_apply -> Basis.dualBasis_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (m : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) m) i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Finite.{succ u3} ι] (i : ι) (m : M), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) i) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, max (succ u1) (succ u2)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b _inst_5) i) m) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.repr.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) m) i)
+Case conversion may be inaccurate. Consider using '#align basis.dual_basis_apply Basis.dualBasis_applyₓ'. -/
 theorem dualBasis_apply (i : ι) (m : M) : b.dualBasis i m = b.repr m i :=
   b.toDual_apply_right i m
 #align basis.dual_basis_apply Basis.dualBasis_apply
 
+#print Basis.coe_dualBasis /-
 @[simp]
 theorem coe_dualBasis : ⇑b.dualBasis = b.Coord :=
   by
   ext (i x)
   apply dual_basis_apply
 #align basis.coe_dual_basis Basis.coe_dualBasis
+-/
 
+#print Basis.toDual_toDual /-
 @[simp]
 theorem toDual_toDual : b.dualBasis.toDual.comp b.toDual = Dual.eval R M :=
   by
@@ -456,13 +651,26 @@ theorem toDual_toDual : b.dualBasis.toDual.comp b.toDual = Dual.eval R M :=
   rw [LinearMap.comp_apply, to_dual_apply_left, coe_to_dual_self, ← coe_dual_basis, dual.eval_apply,
     Basis.repr_self, Finsupp.single_apply, dual_basis_apply_self]
 #align basis.to_dual_to_dual Basis.toDual_toDual
+-/
 
 end Finite
 
+/- warning: basis.dual_basis_equiv_fun -> Basis.dualBasis_equivFun is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Fintype.{u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> ι -> R) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u3 u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) (Pi.Function.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.equivFun.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)) _inst_5 (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b (Finite.of_fintype.{u3} ι _inst_5))) l i) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : DecidableEq.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : Fintype.{u3} ι] (l : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ u1} R (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u2), max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (ι -> R) (AddMonoid.toZero.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (ι -> R) (AddMonoid.toAddZeroClass.{max u1 u3} (ι -> R) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, max u1 u2, max u1 u3} (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (ι -> R) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u3, max (max u1 u2) u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearEquiv.{u1, u1, max u1 u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u3} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ι -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Pi.module.{u3, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : ι) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Basis.equivFun.{u3, u1, max u1 u2} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) _inst_5 (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) b (Finite.of_fintype.{u3} ι _inst_5))) l i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) l (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i))
+Case conversion may be inaccurate. Consider using '#align basis.dual_basis_equiv_fun Basis.dualBasis_equivFunₓ'. -/
 theorem dualBasis_equivFun [Fintype ι] (l : Dual R M) (i : ι) :
     b.dualBasis.equivFun l i = l (b i) := by rw [Basis.equivFun_apply, dual_basis_repr]
 #align basis.dual_basis_equiv_fun Basis.dualBasis_equivFun
 
+/- warning: basis.eval_ker -> Basis.eval_ker is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, max u2 u1, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.eval.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Bot.bot.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {ι : Type.{u1}}, (Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) -> (Eq.{succ u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u3, max u2 u3, max u2 u3} R R M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u3, max u3 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u2 u3} R R M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.Dual.eval.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)) (Bot.bot.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align basis.eval_ker Basis.eval_kerₓ'. -/
 theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   by
   rw [ker_eq_bot']
@@ -471,6 +679,12 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) : (Dual.eval R M).ker = ⊥ :=
   exact (Basis.forall_coord_eq_zero_iff _).mp fun i => hm (b.coord i)
 #align basis.eval_ker Basis.eval_ker
 
+/- warning: basis.eval_range -> Basis.eval_range is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_5 : Finite.{succ u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, u2, max u2 u1, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u2 u1} R R M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Top.top.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Submodule.hasTop.{u1, max u2 u1} R (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.Dual.eval._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {ι : Type.{u1}} [_inst_5 : Finite.{succ u1} ι], (Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) -> (Eq.{max (succ u2) (succ u3)} (Submodule.{u2, max u2 u3} R (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.range.{u2, u2, u3, max u2 u3, max u2 u3} R R M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u3, max u3 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u2 u3} R R M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.eval.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)) (Top.top.{max u2 u3} (Submodule.{u2, max u2 u3} R (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.instTopSubmodule.{u2, max u2 u3} R (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))
+Case conversion may be inaccurate. Consider using '#align basis.eval_range Basis.eval_rangeₓ'. -/
 theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).range = ⊤ := by
   classical
     cases nonempty_fintype ι
@@ -478,11 +692,19 @@ theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) : (eval R M).ran
     infer_instance
 #align basis.eval_range Basis.eval_range
 
+#print Basis.evalEquiv /-
 /-- A module with a basis is linearly equivalent to the dual of its dual space. -/
 def evalEquiv {ι : Type _} [Finite ι] (b : Basis ι R M) : M ≃ₗ[R] Dual R (Dual R M) :=
   LinearEquiv.ofBijective (eval R M) ⟨ker_eq_bot.mp b.eval_ker, range_eq_top.mp b.eval_range⟩
 #align basis.eval_equiv Basis.evalEquiv
+-/
 
+/- warning: basis.eval_equiv_to_linear_map -> Basis.evalEquiv_toLinearMap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_5 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{max (succ u2) (succ (max u2 u1))} (LinearMap.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.evalEquiv._proof_4.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.evalEquiv._proof_1.{u1} R _inst_1) (Basis.evalEquiv._proof_2.{u1} R _inst_1) M (Module.Dual.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, u1} R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (LinearMap.module.{u1, u1, u1, max u2 u1, u1} R R R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Basis.evalEquiv._proof_3.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.evalEquiv._proof_4.{u1} R _inst_1)) (Basis.evalEquiv.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι _inst_5 b)) (Module.Dual.eval.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {ι : Type.{u1}} [_inst_5 : Finite.{succ u1} ι] (b : Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3), Eq.{max (succ u2) (succ u3)} (LinearMap.{u2, u2, u3, max u2 u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearEquiv.toLinearMap.{u2, u2, u3, max u2 u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) M (Module.Dual.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (CommRing.toCommSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (LinearMap.addCommMonoid.{u2, u2, max u2 u3, u2} R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u2 u3, u2} R R R (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Basis.evalEquiv.{u2, u3, u1} R M _inst_1 _inst_2 _inst_3 ι _inst_5 b)) (Module.Dual.eval.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)
+Case conversion may be inaccurate. Consider using '#align basis.eval_equiv_to_linear_map Basis.evalEquiv_toLinearMapₓ'. -/
 @[simp]
 theorem evalEquiv_toLinearMap {ι : Type _} [Finite ι] (b : Basis ι R M) :
     b.evalEquiv.toLinearMap = Dual.eval R M :=
@@ -495,18 +717,28 @@ open Classical
 
 variable [Finite R M] [Free R M] [Nontrivial R]
 
+#print Basis.dual_free /-
 instance dual_free : Free R (Dual R M) :=
   Free.of_basis (Free.chooseBasis R M).dualBasis
 #align basis.dual_free Basis.dual_free
+-/
 
+#print Basis.dual_finite /-
 instance dual_finite : Finite R (Dual R M) :=
   Finite.of_basis (Free.chooseBasis R M).dualBasis
 #align basis.dual_finite Basis.dual_finite
+-/
 
 end
 
 end CommRing
 
+/- warning: basis.total_coord -> Basis.total_coord is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1)))))) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1))))) (Basis.coord.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b)) f) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) b i)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) f i)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Finite.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) f) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u3, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} R R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Finsupp.total.{u3, max u2 u1, u1} ι (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Basis.coord.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b)) f) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) b i)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) f i)
+Case conversion may be inaccurate. Consider using '#align basis.total_coord Basis.total_coordₓ'. -/
 /-- `simp` normal form version of `total_dual_basis` -/
 @[simp]
 theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b : Basis ι R M)
@@ -516,6 +748,12 @@ theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b :
   rw [← coe_dual_basis, total_dual_basis]
 #align basis.total_coord Basis.total_coord
 
+/- warning: basis.dual_rank_eq -> Basis.dual_rank_eq is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : Finite.{succ u3} ι], (Basis.{u3, u1, u2} ι K V (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Cardinal.lift.{u1, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Module.rank.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (CommRing.toCommSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K _inst_1)))) (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1)) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (CommRing.toRing.{u1} K _inst_1))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K _inst_1) (Monoid.toMulAction.{u1} K (CommMonoid.toMonoid.{u1} K (CommRing.toCommMonoid.{u1} K _inst_1)))))))
+but is expected to have type
+  forall {K : Type.{u2}} {V : Type.{u3}} {ι : Type.{u1}} [_inst_1 : CommRing.{u2} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} K V (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : Finite.{succ u1} ι], (Basis.{u1, u2, u3} ι K V (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) -> (Eq.{max (succ (succ u2)) (succ (succ u3))} Cardinal.{max u3 u2} (Cardinal.lift.{u2, u3} (Module.rank.{u2, u3} K V (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) (Module.rank.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V (CommRing.toCommSemiring.{u2} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)))) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (smulCommClass_self.{u2, u2} K K (CommRing.toCommMonoid.{u2} K _inst_1) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align basis.dual_rank_eq Basis.dual_rank_eqₓ'. -/
 theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
     Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by
   classical
@@ -540,16 +778,21 @@ section
 
 variable (K) (V)
 
+#print Module.eval_ker /-
 theorem eval_ker : (eval K V).ker = ⊥ := by classical exact (Basis.ofVectorSpace K V).eval_ker
 #align module.eval_ker Module.eval_ker
+-/
 
+#print Module.map_eval_injective /-
 theorem map_eval_injective : (Submodule.map (eval K V)).Injective :=
   by
   apply Submodule.map_injective_of_injective
   rw [← LinearMap.ker_eq_bot]
   apply eval_ker K V
 #align module.map_eval_injective Module.map_eval_injective
+-/
 
+#print Module.comap_eval_surjective /-
 -- elaborates faster than `exact`
 theorem comap_eval_surjective : (Submodule.comap (eval K V)).Surjective :=
   by
@@ -557,6 +800,7 @@ theorem comap_eval_surjective : (Submodule.comap (eval K V)).Surjective :=
   rw [← LinearMap.ker_eq_bot]
   apply eval_ker K V
 #align module.comap_eval_surjective Module.comap_eval_surjective
+-/
 
 -- elaborates faster than `exact`
 end
@@ -565,14 +809,24 @@ section
 
 variable (K)
 
+#print Module.eval_apply_eq_zero_iff /-
 theorem eval_apply_eq_zero_iff (v : V) : (eval K V) v = 0 ↔ v = 0 := by
   simpa only using set_like.ext_iff.mp (eval_ker K V) v
 #align module.eval_apply_eq_zero_iff Module.eval_apply_eq_zero_iff
+-/
 
+#print Module.eval_apply_injective /-
 theorem eval_apply_injective : Function.Injective (eval K V) :=
   (injective_iff_map_eq_zero' (eval K V)).mpr (eval_apply_eq_zero_iff K)
 #align module.eval_apply_injective Module.eval_apply_injective
+-/
 
+/- warning: module.forall_dual_apply_eq_zero_iff -> Module.forall_dual_apply_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) (Eq.{succ u2} V v (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2)))))))))
+but is expected to have type
+  forall (K : Type.{u1}) {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) _inst_1))))))) (Eq.{succ u2} V v (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align module.forall_dual_apply_eq_zero_iff Module.forall_dual_apply_eq_zero_iffₓ'. -/
 theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v = 0) ↔ v = 0 :=
   by
   rw [← eval_apply_eq_zero_iff K v, LinearMap.ext_iff]
@@ -581,19 +835,24 @@ theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v
 
 end
 
+#print Module.dual_rank_eq /-
 -- TODO(jmc): generalize to rings, once `module.rank` is generalized
 theorem dual_rank_eq [FiniteDimensional K V] :
     Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) :=
   (Basis.ofVectorSpace K V).dual_rank_eq
 #align module.dual_rank_eq Module.dual_rank_eq
+-/
 
+#print Module.erange_coe /-
 theorem erange_coe [FiniteDimensional K V] : (eval K V).range = ⊤ :=
   letI : IsNoetherian K V := IsNoetherian.iff_fg.2 inferInstance
   (Basis.ofVectorSpace K V).eval_range
 #align module.erange_coe Module.erange_coe
+-/
 
 variable (K V)
 
+#print Module.evalEquiv /-
 /-- A vector space is linearly equivalent to the dual of its dual space. -/
 def evalEquiv [FiniteDimensional K V] : V ≃ₗ[K] Dual K (Dual K V) :=
   LinearEquiv.ofBijective
@@ -602,31 +861,40 @@ def evalEquiv [FiniteDimensional K V] : V ≃ₗ[K] Dual K (Dual K V) :=
       rw [← ker_eq_bot]
       apply eval_ker K V, range_eq_top.mp erange_coe⟩
 #align module.eval_equiv Module.evalEquiv
+-/
 
+#print Module.mapEvalEquiv /-
 /-- The isomorphism `module.eval_equiv` induces an order isomorphism on subspaces. -/
 def mapEvalEquiv [FiniteDimensional K V] : Subspace K V ≃o Subspace K (Dual K (Dual K V)) :=
   Submodule.orderIsoMapComap (evalEquiv K V)
 #align module.map_eval_equiv Module.mapEvalEquiv
+-/
 
 variable {K V}
 
+#print Module.evalEquiv_toLinearMap /-
 @[simp]
 theorem evalEquiv_toLinearMap [FiniteDimensional K V] :
     (evalEquiv K V).toLinearMap = Dual.eval K V :=
   rfl
 #align module.eval_equiv_to_linear_map Module.evalEquiv_toLinearMap
+-/
 
+#print Module.mapEvalEquiv_apply /-
 @[simp]
 theorem mapEvalEquiv_apply [FiniteDimensional K V] (W : Subspace K V) :
     mapEvalEquiv K V W = W.map (eval K V) :=
   rfl
 #align module.map_eval_equiv_apply Module.mapEvalEquiv_apply
+-/
 
+#print Module.mapEvalEquiv_symm_apply /-
 @[simp]
 theorem mapEvalEquiv_symm_apply [FiniteDimensional K V] (W'' : Subspace K (Dual K (Dual K V))) :
     (mapEvalEquiv K V).symm W'' = W''.comap (eval K V) :=
   rfl
 #align module.map_eval_equiv_symm_apply Module.mapEvalEquiv_symm_apply
+-/
 
 end Module
 
@@ -646,6 +914,7 @@ unsafe def use_finite_instance : tactic Unit :=
   sorry
 #align use_finite_instance use_finite_instance
 
+#print Module.DualBases /-
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic use_finite_instance -/
 /-- `e` and `ε` have characteristic properties of a basis and its dual -/
 @[nolint has_nonempty_instance]
@@ -656,6 +925,7 @@ structure Module.DualBases (e : ι → M) (ε : ι → Dual R M) : Prop where
     run_tac
       use_finite_instance
 #align module.dual_bases Module.DualBases
+-/
 
 end DualBases
 
@@ -669,6 +939,12 @@ variable [CommRing R] [AddCommGroup M] [Module R M]
 
 variable {e : ι → M} {ε : ι → Dual R M}
 
+/- warning: module.dual_bases.coeffs -> Module.DualBases.coeffs is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> M -> (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.coeffs Module.DualBases.coeffsₓ'. -/
 /-- The coefficients of `v` on the basis `e` -/
 def coeffs [DecidableEq ι] (h : DualBases e ε) (m : M) : ι →₀ R
     where
@@ -679,17 +955,35 @@ def coeffs [DecidableEq ι] (h : DualBases e ε) (m : M) : ι →₀ R
     rw [Set.Finite.mem_toFinset, Set.mem_setOf_eq]
 #align module.dual_bases.coeffs Module.DualBases.coeffs
 
+/- warning: module.dual_bases.coeffs_apply -> Module.DualBases.coeffs_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (m : M) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.DualBases.coeffs.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h m) i) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ε i) m)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (m : M) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Module.DualBases.coeffs.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h m) i) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ε i) m)
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.coeffs_apply Module.DualBases.coeffs_applyₓ'. -/
 @[simp]
 theorem coeffs_apply [DecidableEq ι] (h : DualBases e ε) (m : M) (i : ι) : h.coeffs m i = ε i m :=
   rfl
 #align module.dual_bases.coeffs_apply Module.DualBases.coeffs_apply
 
+/- warning: module.dual_bases.lc -> Module.DualBases.lc is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}}, (ι -> M) -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> M
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}}, (ι -> M) -> (Finsupp.{u3, u1} ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) -> M
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.lc Module.DualBases.lcₓ'. -/
 /-- linear combinations of elements of `e`.
 This is a convenient abbreviation for `finsupp.total _ M R e l` -/
 def lc {ι} (e : ι → M) (l : ι →₀ R) : M :=
   l.Sum fun (i : ι) (a : R) => a • e i
 #align module.dual_bases.lc Module.DualBases.lc
 
+/- warning: module.dual_bases.lc_def -> Module.DualBases.lc_def is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (e : ι -> M) (l : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{succ u2} M (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e l) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearMap.{u1, u1, max u3 u1, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3) (fun (_x : LinearMap.{u1, u1, max u3 u1, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3) => (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> M) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Finsupp.total.{u3, u2, u1} ι M R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e) l)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (e : ι -> M) (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))), Eq.{succ u1} M (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearMap.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _inst_3) (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u3, u1} R R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finsupp.module.{u3, u2, u2} ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.total.{u3, u1, u2} ι M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e) l)
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.lc_def Module.DualBases.lc_defₓ'. -/
 theorem lc_def (e : ι → M) (l : ι →₀ R) : lc e l = Finsupp.total _ _ _ e l :=
   rfl
 #align module.dual_bases.lc_def Module.DualBases.lc_def
@@ -700,6 +994,12 @@ variable [DecidableEq ι] (h : DualBases e ε)
 
 include h
 
+/- warning: module.dual_bases.dual_lc -> Module.DualBases.dual_lc is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> (forall (l : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (i : ι), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ε i) (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) l i))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> (forall (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ε i) (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) l i))
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.dual_lc Module.DualBases.dual_lcₓ'. -/
 theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i :=
   by
   erw [LinearMap.map_sum]
@@ -712,6 +1012,12 @@ theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i :=
     simp [Finsupp.not_mem_support_iff.1 p_not_in]
 #align module.dual_bases.dual_lc Module.DualBases.dual_lc
 
+/- warning: module.dual_bases.coeffs_lc -> Module.DualBases.coeffs_lc is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (l : Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))), Eq.{max (succ u3) (succ u1)} (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Module.DualBases.coeffs.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) l
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (l : Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))), Eq.{max (succ u2) (succ u3)} (Finsupp.{u3, u2} ι R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Module.DualBases.coeffs.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h (Module.DualBases.lc.{u2, u1, u3} R M _inst_1 _inst_2 _inst_3 ι e l)) l
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.coeffs_lc Module.DualBases.coeffs_lcₓ'. -/
 @[simp]
 theorem coeffs_lc (l : ι →₀ R) : h.coeffs (DualBases.lc e l) = l :=
   by
@@ -719,6 +1025,12 @@ theorem coeffs_lc (l : ι →₀ R) : h.coeffs (DualBases.lc e l) = l :=
   rw [h.coeffs_apply, h.dual_lc]
 #align module.dual_bases.coeffs_lc Module.DualBases.coeffs_lc
 
+/- warning: module.dual_bases.lc_coeffs -> Module.DualBases.lc_coeffs is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (m : M), Eq.{succ u2} M (Module.DualBases.lc.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι e (Module.DualBases.coeffs.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h m)) m
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u3}} {ι : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u3} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u1} ι] (h : Module.DualBases.{u2, u3, u1} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) (m : M), Eq.{succ u3} M (Module.DualBases.lc.{u2, u3, u1} R M _inst_1 _inst_2 _inst_3 ι e (Module.DualBases.coeffs.{u2, u3, u1} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h m)) m
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.lc_coeffs Module.DualBases.lc_coeffsₓ'. -/
 /-- For any m : M n, \sum_{p ∈ Q n} (ε p m) • e p = m -/
 @[simp]
 theorem lc_coeffs (m : M) : DualBases.lc e (h.coeffs m) = m :=
@@ -728,6 +1040,7 @@ theorem lc_coeffs (m : M) : DualBases.lc e (h.coeffs m) = m :=
   simp [-sub_eq_add_neg, LinearMap.map_sub, h.dual_lc, sub_eq_zero]
 #align module.dual_bases.lc_coeffs Module.DualBases.lc_coeffs
 
+#print Module.DualBases.basis /-
 /-- `(h : dual_bases e ε).basis` shows the family of vectors `e` forms a basis. -/
 @[simps]
 def basis : Basis ι R M :=
@@ -743,7 +1056,14 @@ def basis : Basis ι R M :=
         ext i
         exact (ε i).map_smul c v }
 #align module.dual_bases.basis Module.DualBases.basis
+-/
 
+/- warning: module.dual_bases.coe_basis -> Module.DualBases.coe_basis is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε), Eq.{max (succ u3) (succ u2)} (ι -> M) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Module.DualBases.basis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h)) e
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u3}} {ι : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u3} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u2} ι] (h : Module.DualBases.{u1, u3, u2} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε), Eq.{max (succ u3) (succ u2)} (forall (a : ι), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u2, succ u3} (Basis.{u2, u1, u3} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u2, u1, u3} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3) (Module.DualBases.basis.{u1, u3, u2} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h)) e
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.coe_basis Module.DualBases.coe_basisₓ'. -/
 @[simp]
 theorem coe_basis : ⇑h.Basis = e := by
   ext i
@@ -753,6 +1073,12 @@ theorem coe_basis : ⇑h.Basis = e := by
   convert if_congr eq_comm rfl rfl
 #align module.dual_bases.coe_basis Module.DualBases.coe_basis
 
+/- warning: module.dual_bases.mem_of_mem_span -> Module.DualBases.mem_of_mem_span is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> (forall {H : Set.{u3} ι} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.image.{u3, u2} ι M e H))) -> (forall (i : ι), (Ne.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ε i) x) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) -> (Membership.Mem.{u3, u3} ι (Set.{u3} ι) (Set.hasMem.{u3} ι) i H)))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι], (Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) -> (forall {H : Set.{u3} ι} {x : M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Set.image.{u3, u2} ι M e H))) -> (forall (i : ι), (Ne.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ε i) x) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) x) _inst_1)))))) -> (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i H)))
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_spanₓ'. -/
 -- `convert` to get rid of a `decidable_eq` mismatch
 theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '' H)) :
     ∀ i : ι, ε i x ≠ 0 → i ∈ H := by
@@ -762,6 +1088,12 @@ theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '
   rwa [← lc_def, h.dual_lc] at hi
 #align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_span
 
+/- warning: module.dual_bases.coe_dual_basis -> Module.DualBases.coe_dualBasis is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u1, u2, u3} R M ι (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) [_inst_5 : Fintype.{u3} ι], Eq.{max (succ u3) (succ (max u2 u1))} (ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (coeFn.{max (succ u3) (succ u1) (succ (max u2 u1)), max (succ u3) (succ (max u2 u1))} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) (fun (_x : Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ (max u2 u1)), succ u3, succ (max u2 u1)} (Basis.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Basis.funLike.{u3, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.dualBasis._proof_1.{u1} R _inst_1)))) (Basis.dualBasis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) (Module.DualBases.basis.{u1, u2, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h) (Finite.of_fintype.{u3} ι _inst_5))) ε
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} {ι : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {e : ι -> M} {ε : ι -> (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)} [_inst_4 : DecidableEq.{succ u3} ι] (h : Module.DualBases.{u2, u1, u3} R M ι (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) e ε) [_inst_5 : Fintype.{u3} ι], Eq.{max (max (succ u2) (succ u1)) (succ u3)} (forall (a : ι), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) a) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u3, max (succ u2) (succ u1)} (Basis.{u3, u2, max u1 u2} ι R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) _x) (Basis.funLike.{u3, u2, max u2 u1} ι R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Basis.dualBasis.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 (fun (a : ι) (b : ι) => _inst_4 a b) (Module.DualBases.basis.{u2, u1, u3} R M ι _inst_1 _inst_2 _inst_3 e ε (fun (a : ι) (b : ι) => _inst_4 a b) h) (Finite.of_fintype.{u3} ι _inst_5))) ε
+Case conversion may be inaccurate. Consider using '#align module.dual_bases.coe_dual_basis Module.DualBases.coe_dualBasisₓ'. -/
 theorem coe_dualBasis [Fintype ι] : ⇑h.Basis.dualBasis = ε :=
   funext fun i =>
     h.Basis.ext fun j => by
@@ -778,30 +1110,48 @@ variable {R : Type u} {M : Type v} [CommSemiring R] [AddCommMonoid M] [Module R
 
 variable {W : Submodule R M}
 
+#print Submodule.dualRestrict /-
 /-- The `dual_restrict` of a submodule `W` of `M` is the linear map from the
   dual of `M` to the dual of `W` such that the domain of each linear map is
   restricted to `W`. -/
 def dualRestrict (W : Submodule R M) : Module.Dual R M →ₗ[R] Module.Dual R W :=
   LinearMap.domRestrict' W
 #align submodule.dual_restrict Submodule.dualRestrict
+-/
 
+#print Submodule.dualRestrict_def /-
 theorem dualRestrict_def (W : Submodule R M) : W.dualRestrict = W.Subtype.dualMap :=
   rfl
 #align submodule.dual_restrict_def Submodule.dualRestrict_def
+-/
 
+/- warning: submodule.dual_restrict_apply -> Submodule.dualRestrict_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1))) => (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualRestrict._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.dualRestrict.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) W) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W))))) x))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => R) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) φ) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) (fun (_x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.Dual.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) x W)) R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Submodule.dualRestrict.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) W)) x))
+Case conversion may be inaccurate. Consider using '#align submodule.dual_restrict_apply Submodule.dualRestrict_applyₓ'. -/
 @[simp]
 theorem dualRestrict_apply (W : Submodule R M) (φ : Module.Dual R M) (x : W) :
     W.dualRestrict φ x = φ (x : M) :=
   rfl
 #align submodule.dual_restrict_apply Submodule.dualRestrict_apply
 
+#print Submodule.dualAnnihilator /-
 /-- The `dual_annihilator` of a submodule `W` is the set of linear maps `φ` such
   that `φ w = 0` for all `w ∈ W`. -/
 def dualAnnihilator {R : Type u} {M : Type v} [CommSemiring R] [AddCommMonoid M] [Module R M]
     (W : Submodule R M) : Submodule R <| Module.Dual R M :=
   W.dualRestrict.ker
 #align submodule.dual_annihilator Submodule.dualAnnihilator
+-/
 
+/- warning: submodule.mem_dual_annihilator -> Submodule.mem_dualAnnihilator is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Iff (Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1)))) φ (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)) (forall (w : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) w W) -> (Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (_x : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ w) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {W : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3), Iff (Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.setLike.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) φ (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)) (forall (w : M), (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)) w W) -> (Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u1, u2} R M _inst_1 _inst_2 _inst_3) φ w) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) w) _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_dual_annihilator Submodule.mem_dualAnnihilatorₓ'. -/
 @[simp]
 theorem mem_dualAnnihilator (φ : Module.Dual R M) : φ ∈ W.dualAnnihilator ↔ ∀ w ∈ W, φ w = 0 :=
   by
@@ -810,24 +1160,36 @@ theorem mem_dualAnnihilator (φ : Module.Dual R M) : φ ∈ W.dualAnnihilator 
   exact ⟨fun h w hw => h ⟨w, hw⟩, fun h w => h w.1 w.2⟩
 #align submodule.mem_dual_annihilator Submodule.mem_dualAnnihilator
 
+#print Submodule.dualRestrict_ker_eq_dualAnnihilator /-
 /-- That $\operatorname{ker}(\iota^* : V^* \to W^*) = \operatorname{ann}(W)$.
 This is the definition of the dual annihilator of the submodule $W$. -/
 theorem dualRestrict_ker_eq_dualAnnihilator (W : Submodule R M) :
     W.dualRestrict.ker = W.dualAnnihilator :=
   rfl
 #align submodule.dual_restrict_ker_eq_dual_annihilator Submodule.dualRestrict_ker_eq_dualAnnihilator
+-/
 
+#print Submodule.dualCoannihilator /-
 /-- The `dual_annihilator` of a submodule of the dual space pulled back along the evaluation map
 `module.dual.eval`. -/
 def dualCoannihilator (Φ : Submodule R (Module.Dual R M)) : Submodule R M :=
   Φ.dualAnnihilator.comap (Module.Dual.eval R M)
 #align submodule.dual_coannihilator Submodule.dualCoannihilator
+-/
 
+#print Submodule.mem_dualCoannihilator /-
 theorem mem_dualCoannihilator {Φ : Submodule R (Module.Dual R M)} (x : M) :
     x ∈ Φ.dualCoannihilator ↔ ∀ φ ∈ Φ, (φ x : R) = 0 := by
   simp_rw [dual_coannihilator, mem_comap, mem_dual_annihilator, Module.Dual.eval_apply]
 #align submodule.mem_dual_coannihilator Submodule.mem_dualCoannihilator
+-/
 
+/- warning: submodule.dual_annihilator_gc -> Submodule.dualAnnihilator_gc is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_4 : CommSemiring.{u1} R] [_inst_5 : AddCommMonoid.{u2} M] [_inst_6 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5], GaloisConnection.{u2, max u2 u1} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6)))) (OrderDual.preorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))))) (Function.comp.{succ u2, succ (max u2 u1), succ (max u2 u1)} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (Equiv.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) (fun (_x : Equiv.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) => (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) -> (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) (Equiv.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))) (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) (OrderDual.toDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_4 _inst_5 _inst_6)) (Function.comp.{succ (max u2 u1), succ (max u2 u1), succ u2} (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualCoannihilator._proof_1.{u1} R _inst_4))) (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 _inst_6) (Submodule.dualCoannihilator.{u1, u2} R M _inst_4 _inst_5 _inst_6) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (Equiv.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (fun (_x : Equiv.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) => (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) -> (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Equiv.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4)))) (OrderDual.ofDual.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u1} R _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)))) _inst_6 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4))) (CommSemiring.toSemiring.{u1} R _inst_4) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_4)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_4))))))
+but is expected to have type
+  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_4 : CommSemiring.{u2} R] [_inst_5 : AddCommMonoid.{u1} M] [_inst_6 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5], GaloisConnection.{u1, max u2 u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (Submodule.completeLattice.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6)))) (OrderDual.preorder.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (Submodule.completeLattice.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))))) (Function.comp.{succ u1, succ (max u2 u1), succ (max u2 u1)} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (Equiv.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (fun (_x : Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) => OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) _x) (Equiv.instFunLikeEquiv.{succ (max u2 u1), succ (max u2 u1)} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))) (OrderDual.toDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))) (Submodule.dualAnnihilator.{u2, u1} R M _inst_4 _inst_5 _inst_6)) (Function.comp.{max (succ u2) (succ u1), max (succ u1) (succ u2), succ u1} (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 _inst_6) (Submodule.dualCoannihilator.{u2, u1} R M _inst_4 _inst_5 _inst_6) (FunLike.coe.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (Equiv.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (fun (_x : OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) => Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))) _x) (Equiv.instFunLikeEquiv.{succ (max u2 u1), succ (max u2 u1)} (OrderDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))))))) (OrderDual.ofDual.{max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M _inst_4 _inst_5 _inst_6) (CommSemiring.toSemiring.{u2} R _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R _inst_4) _inst_5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)))) _inst_6 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))) (CommSemiring.toSemiring.{u2} R _inst_4) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_4) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_4)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_4))))))))))
+Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_gc Submodule.dualAnnihilator_gcₓ'. -/
 theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Module R M] :
     GaloisConnection
       (OrderDual.toDual ∘ (dualAnnihilator : Submodule R M → Submodule R (Module.Dual R M)))
@@ -845,16 +1207,21 @@ theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Mo
       exact this x hx
 #align submodule.dual_annihilator_gc Submodule.dualAnnihilator_gc
 
+#print Submodule.le_dualAnnihilator_iff_le_dualCoannihilator /-
 theorem le_dualAnnihilator_iff_le_dualCoannihilator {U : Submodule R (Module.Dual R M)}
     {V : Submodule R M} : U ≤ V.dualAnnihilator ↔ V ≤ U.dualCoannihilator :=
   (dualAnnihilator_gc R M).le_iff_le
 #align submodule.le_dual_annihilator_iff_le_dual_coannihilator Submodule.le_dualAnnihilator_iff_le_dualCoannihilator
+-/
 
+#print Submodule.dualAnnihilator_bot /-
 @[simp]
 theorem dualAnnihilator_bot : (⊥ : Submodule R M).dualAnnihilator = ⊤ :=
   (dualAnnihilator_gc R M).l_bot
 #align submodule.dual_annihilator_bot Submodule.dualAnnihilator_bot
+-/
 
+#print Submodule.dualAnnihilator_top /-
 @[simp]
 theorem dualAnnihilator_top : (⊤ : Submodule R M).dualAnnihilator = ⊥ :=
   by
@@ -863,64 +1230,109 @@ theorem dualAnnihilator_top : (⊤ : Submodule R M).dualAnnihilator = ⊥ :=
   simp_rw [mem_dual_annihilator, mem_bot, mem_top, forall_true_left]
   exact fun h => LinearMap.ext h
 #align submodule.dual_annihilator_top Submodule.dualAnnihilator_top
+-/
 
+#print Submodule.dualCoannihilator_bot /-
 @[simp]
 theorem dualCoannihilator_bot : (⊥ : Submodule R (Module.Dual R M)).dualCoannihilator = ⊤ :=
   (dualAnnihilator_gc R M).u_top
 #align submodule.dual_coannihilator_bot Submodule.dualCoannihilator_bot
+-/
 
+/- warning: submodule.dual_annihilator_anti -> Submodule.dualAnnihilator_anti is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3} {V : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))) U V) -> (LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 V) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3} {V : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))) U V) -> (LE.le.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Preorder.toLE.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Submodule.completeLattice.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 V) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U))
+Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_anti Submodule.dualAnnihilator_antiₓ'. -/
 @[mono]
 theorem dualAnnihilator_anti {U V : Submodule R M} (hUV : U ≤ V) :
     V.dualAnnihilator ≤ U.dualAnnihilator :=
   (dualAnnihilator_gc R M).monotone_l hUV
 #align submodule.dual_annihilator_anti Submodule.dualAnnihilator_anti
 
+#print Submodule.dualCoannihilator_anti /-
 @[mono]
 theorem dualCoannihilator_anti {U V : Submodule R (Module.Dual R M)} (hUV : U ≤ V) :
     V.dualCoannihilator ≤ U.dualCoannihilator :=
   (dualAnnihilator_gc R M).monotone_u hUV
 #align submodule.dual_coannihilator_anti Submodule.dualCoannihilator_anti
+-/
 
+/- warning: submodule.le_dual_annihilator_dual_coannihilator -> Submodule.le_dualAnnihilator_dualCoannihilator is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3), LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))) U (Submodule.dualCoannihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3), LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))))) U (Submodule.dualCoannihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U))
+Case conversion may be inaccurate. Consider using '#align submodule.le_dual_annihilator_dual_coannihilator Submodule.le_dualAnnihilator_dualCoannihilatorₓ'. -/
 theorem le_dualAnnihilator_dualCoannihilator (U : Submodule R M) :
     U ≤ U.dualAnnihilator.dualCoannihilator :=
   (dualAnnihilator_gc R M).le_u_l U
 #align submodule.le_dual_annihilator_dual_coannihilator Submodule.le_dualAnnihilator_dualCoannihilator
 
+#print Submodule.le_dualCoannihilator_dualAnnihilator /-
 theorem le_dualCoannihilator_dualAnnihilator (U : Submodule R (Module.Dual R M)) :
     U ≤ U.dualCoannihilator.dualAnnihilator :=
   (dualAnnihilator_gc R M).l_u_le U
 #align submodule.le_dual_coannihilator_dual_annihilator Submodule.le_dualCoannihilator_dualAnnihilator
+-/
 
+#print Submodule.dualAnnihilator_dualCoannihilator_dualAnnihilator /-
 theorem dualAnnihilator_dualCoannihilator_dualAnnihilator (U : Submodule R M) :
     U.dualAnnihilator.dualCoannihilator.dualAnnihilator = U.dualAnnihilator :=
   (dualAnnihilator_gc R M).l_u_l_eq_l U
 #align submodule.dual_annihilator_dual_coannihilator_dual_annihilator Submodule.dualAnnihilator_dualCoannihilator_dualAnnihilator
+-/
 
+#print Submodule.dualCoannihilator_dualAnnihilator_dualCoannihilator /-
 theorem dualCoannihilator_dualAnnihilator_dualCoannihilator (U : Submodule R (Module.Dual R M)) :
     U.dualCoannihilator.dualAnnihilator.dualCoannihilator = U.dualCoannihilator :=
   (dualAnnihilator_gc R M).u_l_u_eq_u U
 #align submodule.dual_coannihilator_dual_annihilator_dual_coannihilator Submodule.dualCoannihilator_dualAnnihilator_dualCoannihilator
+-/
 
+#print Submodule.dualAnnihilator_sup_eq /-
 theorem dualAnnihilator_sup_eq (U V : Submodule R M) :
     (U ⊔ V).dualAnnihilator = U.dualAnnihilator ⊓ V.dualAnnihilator :=
   (dualAnnihilator_gc R M).l_sup
 #align submodule.dual_annihilator_sup_eq Submodule.dualAnnihilator_sup_eq
+-/
 
+#print Submodule.dualCoannihilator_sup_eq /-
 theorem dualCoannihilator_sup_eq (U V : Submodule R (Module.Dual R M)) :
     (U ⊔ V).dualCoannihilator = U.dualCoannihilator ⊓ V.dualCoannihilator :=
   (dualAnnihilator_gc R M).u_inf
 #align submodule.dual_coannihilator_sup_eq Submodule.dualCoannihilator_sup_eq
+-/
 
+/- warning: submodule.dual_annihilator_supr_eq -> Submodule.dualAnnihilator_iSup_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {ι : Type.{u3}} (U : ι -> (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)), Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (iSup.{u2, succ u3} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3))) ι (fun (i : ι) => U i))) (iInf.{max u2 u1, succ u3} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.hasInf.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (U i)))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] {ι : Type.{u1}} (U : ι -> (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)), Eq.{max (succ u2) (succ u3)} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (iSup.{u3, succ u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) ι (fun (i : ι) => U i))) (iInf.{max u2 u3, succ u1} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.instInfSetSubmodule.{u2, max u2 u3} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (U i)))
+Case conversion may be inaccurate. Consider using '#align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eqₓ'. -/
 theorem dualAnnihilator_iSup_eq {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, U i).dualAnnihilator = ⨅ i : ι, (U i).dualAnnihilator :=
   (dualAnnihilator_gc R M).l_iSup
 #align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eq
 
+/- warning: submodule.dual_coannihilator_supr_eq -> Submodule.dualCoannihilator_iSup_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {ι : Type.{u3}} (U : ι -> (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1))))))), Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.dualCoannihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (iSup.{max u2 u1, succ u3} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommSemiring.toCommMonoid.{u1} R _inst_1)))))))) ι (fun (i : ι) => U i))) (iInf.{u2, succ u3} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (i : ι) => Submodule.dualCoannihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (U i)))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] {ι : Type.{u1}} (U : ι -> (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))))), Eq.{succ u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Submodule.dualCoannihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (iSup.{max u2 u3, succ u1} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.completeLattice.{u2, max u2 u3} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) ι (fun (i : ι) => U i))) (iInf.{u3, succ u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Submodule.instInfSetSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) ι (fun (i : ι) => Submodule.dualCoannihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (U i)))
+Case conversion may be inaccurate. Consider using '#align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eqₓ'. -/
 theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.Dual R M)) :
     (⨆ i : ι, U i).dualCoannihilator = ⨅ i : ι, (U i).dualCoannihilator :=
   (dualAnnihilator_gc R M).u_iInf
 #align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
 
+/- warning: submodule.sup_dual_annihilator_le_inf -> Submodule.sup_dualAnnihilator_le_inf is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (V : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3), LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))))) (Sup.sup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (SemilatticeSup.toHasSup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Lattice.toSemilatticeSup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (ConditionallyCompleteLattice.toLattice.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 V)) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Inf.inf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) U V))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] (U : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (V : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3), LE.le.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Preorder.toLE.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Submodule.completeLattice.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (Sup.sup.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SemilatticeSup.toSup.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Submodule.completeLattice.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 U) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 V)) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Inf.inf.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.instInfSubmodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) U V))
+Case conversion may be inaccurate. Consider using '#align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_infₓ'. -/
 /-- See also `subspace.dual_annihilator_inf_eq` for vector subspaces. -/
 theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
     U.dualAnnihilator ⊔ V.dualAnnihilator ≤ (U ⊓ V).dualAnnihilator :=
@@ -929,6 +1341,12 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
   apply inf_le_inf <;> exact le_dual_annihilator_dual_coannihilator _
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
 
+/- warning: submodule.supr_dual_annihilator_le_infi -> Submodule.iSup_dualAnnihilator_le_iInf is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {ι : Type.{u3}} (U : ι -> (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3)), LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))))) (iSup.{max u2 u1, succ u3} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (ConditionallyCompleteLattice.toHasSup.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.dualAnnihilator._proof_1.{u1} R _inst_1))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (U i))) (Submodule.dualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 (iInf.{u2, succ u3} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_3) ι (fun (i : ι) => U i)))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] {ι : Type.{u1}} (U : ι -> (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)), LE.le.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Preorder.toLE.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.completeLattice.{u2, max u2 u3} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))))) (iSup.{max u2 u3, succ u1} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u2, max u3 u2} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Submodule.completeLattice.{u2, max u2 u3} R (Module.Dual.{u2, u3} R M _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u2} R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} R R R M R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (U i))) (Submodule.dualAnnihilator.{u2, u3} R M _inst_1 _inst_2 _inst_3 (iInf.{u3, succ u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Submodule.instInfSetSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) ι (fun (i : ι) => U i)))
+Case conversion may be inaccurate. Consider using '#align submodule.supr_dual_annihilator_le_infi Submodule.iSup_dualAnnihilator_le_iInfₓ'. -/
 /-- See also `subspace.dual_annihilator_infi_eq` for vector subspaces when `ι` is finite. -/
 theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, (U i).dualAnnihilator) ≤ (⨅ i : ι, U i).dualAnnihilator :=
@@ -949,12 +1367,15 @@ universe u v w
 -- We work in vector spaces because `exists_is_compl` only hold for vector spaces
 variable {K : Type u} {V : Type v} [Field K] [AddCommGroup V] [Module K V]
 
+#print Subspace.dualCoannihilator_top /-
 @[simp]
 theorem dualCoannihilator_top (W : Subspace K V) :
     (⊤ : Subspace K (Module.Dual K W)).dualCoannihilator = ⊥ := by
   rw [dual_coannihilator, dual_annihilator_top, comap_bot, Module.eval_ker]
 #align subspace.dual_coannihilator_top Subspace.dualCoannihilator_top
+-/
 
+#print Subspace.dualAnnihilator_dualCoannihilator_eq /-
 theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
     W.dualAnnihilator.dualCoannihilator = W :=
   by
@@ -981,13 +1402,21 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
   intro v hv
   apply LinearMap.ofIsCompl_left_apply hW ⟨v, hv⟩
 #align subspace.dual_annihilator_dual_coannihilator_eq Subspace.dualAnnihilator_dualCoannihilator_eq
+-/
 
+/- warning: subspace.forall_mem_dual_annihilator_apply_eq_zero_iff -> Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), (Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) φ (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))))) (Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v W)
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (v : V), Iff (forall (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), (Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) φ (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ v) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) v) _inst_1)))))))) (Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v W)
+Case conversion may be inaccurate. Consider using '#align subspace.forall_mem_dual_annihilator_apply_eq_zero_iff Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iffₓ'. -/
 -- exact elaborates slowly
 theorem forall_mem_dualAnnihilator_apply_eq_zero_iff (W : Subspace K V) (v : V) :
     (∀ φ : Module.Dual K V, φ ∈ W.dualAnnihilator → φ v = 0) ↔ v ∈ W := by
   rw [← set_like.ext_iff.mp dual_annihilator_dual_coannihilator_eq v, mem_dual_coannihilator]
 #align subspace.forall_mem_dual_annihilator_apply_eq_zero_iff Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff
 
+#print Subspace.dualAnnihilatorGci /-
 /-- `submodule.dual_annihilator` and `submodule.dual_coannihilator` form a Galois coinsertion. -/
 def dualAnnihilatorGci (K V : Type _) [Field K] [AddCommGroup V] [Module K V] :
     GaloisCoinsertion
@@ -999,12 +1428,20 @@ def dualAnnihilatorGci (K V : Type _) [Field K] [AddCommGroup V] [Module K V] :
   u_l_le W := dualAnnihilator_dualCoannihilator_eq.le
   choice_eq W h := rfl
 #align subspace.dual_annihilator_gci Subspace.dualAnnihilatorGci
+-/
 
+/- warning: subspace.dual_annihilator_le_dual_annihilator_iff -> Subspace.dualAnnihilator_le_dualAnnihilator_iff is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {W' : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Iff (LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.completeLattice.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W')) (LE.le.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) W' W)
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {W' : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Iff (LE.le.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Preorder.toLE.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.completeLattice.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W')) (LE.le.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Preorder.toLE.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) W' W)
+Case conversion may be inaccurate. Consider using '#align subspace.dual_annihilator_le_dual_annihilator_iff Subspace.dualAnnihilator_le_dualAnnihilator_iffₓ'. -/
 theorem dualAnnihilator_le_dualAnnihilator_iff {W W' : Subspace K V} :
     W.dualAnnihilator ≤ W'.dualAnnihilator ↔ W' ≤ W :=
   (dualAnnihilatorGci K V).l_le_l_iff
 #align subspace.dual_annihilator_le_dual_annihilator_iff Subspace.dualAnnihilator_le_dualAnnihilator_iff
 
+#print Subspace.dualAnnihilator_inj /-
 theorem dualAnnihilator_inj {W W' : Subspace K V} :
     W.dualAnnihilator = W'.dualAnnihilator ↔ W = W' :=
   by
@@ -1013,7 +1450,9 @@ theorem dualAnnihilator_inj {W W' : Subspace K V} :
   · rintro rfl
     rfl
 #align subspace.dual_annihilator_inj Subspace.dualAnnihilator_inj
+-/
 
+#print Subspace.dualLift /-
 /-- Given a subspace `W` of `V` and an element of its dual `φ`, `dual_lift W φ` is
 an arbitrary extension of `φ` to an element of the dual of `V`.
 That is, `dual_lift W φ` sends `w ∈ W` to `φ x` and `x` in a chosen complement of `W` to `0`. -/
@@ -1021,9 +1460,16 @@ noncomputable def dualLift (W : Subspace K V) : Module.Dual K W →ₗ[K] Module
   let h := Classical.indefiniteDescription _ W.exists_isCompl
   (LinearMap.ofIsComplProd h.2).comp (LinearMap.inl _ _ _)
 #align subspace.dual_lift Subspace.dualLift
+-/
 
 variable {W : Subspace K V}
 
+/- warning: subspace.dual_lift_of_subtype -> Subspace.dualLift_of_subtype is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} (w : coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W))))) w)) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) -> K) (Module.Dual.hasCoeToFun.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ w)
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} (w : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (SetLike.coe.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) W)) w)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (SetLike.coe.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) W)) w)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ w)
+Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtypeₓ'. -/
 @[simp]
 theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w :=
   by
@@ -1031,17 +1477,31 @@ theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w :
   rfl
 #align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtype
 
+/- warning: subspace.dual_lift_of_mem -> Subspace.dualLift_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} {w : V} (hw : Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) w W), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => V -> K) (Module.Dual.hasCoeToFun.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) w) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) -> K) (Module.Dual.hasCoeToFun.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ (Subtype.mk.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W) w hw))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} {φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)} {w : V} (hw : Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) w W), Eq.{succ u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) V (fun (_x : V) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : V) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) w) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) => K) _x) (Module.Dual.instFunLikeDual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) φ (Subtype.mk.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W) w hw))
+Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_of_mem Subspace.dualLift_of_memₓ'. -/
 theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLift φ w = φ ⟨w, hw⟩ :=
   by convert dual_lift_of_subtype ⟨w, hw⟩
 #align subspace.dual_lift_of_mem Subspace.dualLift_of_mem
 
+#print Subspace.dualRestrict_comp_dualLift /-
 @[simp]
 theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.dualLift = 1 :=
   by
   ext (φ x)
   simp
 #align subspace.dual_restrict_comp_dual_lift Subspace.dualRestrict_comp_dualLift
+-/
 
+/- warning: subspace.dual_restrict_left_inverse -> Subspace.dualRestrict_leftInverse is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.LeftInverse.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.LeftInverse.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
+Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverseₓ'. -/
 theorem dualRestrict_leftInverse (W : Subspace K V) :
     Function.LeftInverse W.dualRestrict W.dualLift := fun x =>
   show W.dualRestrict.comp W.dualLift x = x
@@ -1050,19 +1510,38 @@ theorem dualRestrict_leftInverse (W : Subspace K V) :
     rfl
 #align subspace.dual_restrict_left_inverse Subspace.dualRestrict_leftInverse
 
+/- warning: subspace.dual_lift_right_inverse -> Subspace.dualLift_rightInverse is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.RightInverse.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3), Function.RightInverse.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
+Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_right_inverse Subspace.dualLift_rightInverseₓ'. -/
 theorem dualLift_rightInverse (W : Subspace K V) :
     Function.RightInverse W.dualLift W.dualRestrict :=
   W.dualRestrict_leftInverse
 #align subspace.dual_lift_right_inverse Subspace.dualLift_rightInverse
 
+/- warning: subspace.dual_restrict_surjective -> Subspace.dualRestrict_surjective is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Surjective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Surjective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))
+Case conversion may be inaccurate. Consider using '#align subspace.dual_restrict_surjective Subspace.dualRestrict_surjectiveₓ'. -/
 theorem dualRestrict_surjective : Function.Surjective W.dualRestrict :=
   W.dualLift_rightInverse.Surjective
 #align subspace.dual_restrict_surjective Subspace.dualRestrict_surjective
 
+/- warning: subspace.dual_lift_injective -> Subspace.dualLift_injective is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Injective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3}, Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))
+Case conversion may be inaccurate. Consider using '#align subspace.dual_lift_injective Subspace.dualLift_injectiveₓ'. -/
 theorem dualLift_injective : Function.Injective W.dualLift :=
   W.dualRestrict_leftInverse.Injective
 #align subspace.dual_lift_injective Subspace.dualLift_injective
 
+#print Subspace.quotAnnihilatorEquiv /-
 /-- The quotient by the `dual_annihilator` of a subspace is isomorphic to the
   dual of that subspace. -/
 noncomputable def quotAnnihilatorEquiv (W : Subspace K V) :
@@ -1070,7 +1549,14 @@ noncomputable def quotAnnihilatorEquiv (W : Subspace K V) :
   (quotEquivOfEq _ _ W.dualRestrict_ker_eq_dualAnnihilator).symm.trans <|
     W.dualRestrict.quotKerEquivOfSurjective dualRestrict_surjective
 #align subspace.quot_annihilator_equiv Subspace.quotAnnihilatorEquiv
+-/
 
+/- warning: subspace.quot_annihilator_equiv_apply -> Subspace.quotAnnihilatorEquiv_apply is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{max (succ u2) (succ u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1))) => (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_3.{u1} K _inst_1)) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.quotAnnihilatorEquiv._proof_4.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.quotAnnihilatorEquiv._proof_1.{u1} K _inst_1) (Subspace.quotAnnihilatorEquiv._proof_2.{u1} K _inst_1)) (Subspace.quotAnnihilatorEquiv.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualRestrict._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (φ : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.mk.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (SMulZeroClass.toSMul.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u2, max u1 u2} K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearEquiv.{u1, u1, max (max u1 u2) u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u2} K K (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (HasQuotient.Quotient.{max u2 u1, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.hasQuotient.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.Quotient.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Subspace.quotAnnihilatorEquiv.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)) (LinearMap.addCommGroup.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Ring.toAddCommGroup.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.dualAnnihilator.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.dualRestrict.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) φ)
+Case conversion may be inaccurate. Consider using '#align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_applyₓ'. -/
 @[simp]
 theorem quotAnnihilatorEquiv_apply (W : Subspace K V) (φ : Module.Dual K V) :
     W.quotAnnihilatorEquiv (Submodule.Quotient.mk φ) = W.dualRestrict φ :=
@@ -1079,16 +1565,26 @@ theorem quotAnnihilatorEquiv_apply (W : Subspace K V) (φ : Module.Dual K V) :
   rfl
 #align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_apply
 
+#print Subspace.dualEquivDual /-
 /-- The natural isomorphism from the dual of a subspace `W` to `W.dual_lift.range`. -/
 noncomputable def dualEquivDual (W : Subspace K V) : Module.Dual K W ≃ₗ[K] W.dualLift.range :=
   LinearEquiv.ofInjective _ dualLift_injective
 #align subspace.dual_equiv_dual Subspace.dualEquivDual
+-/
 
+#print Subspace.dualEquivDual_def /-
 theorem dualEquivDual_def (W : Subspace K V) :
     W.dualEquivDual.toLinearMap = W.dualLift.range_restrict :=
   rfl
 #align subspace.dual_equiv_dual_def Subspace.dualEquivDual_def
+-/
 
+/- warning: subspace.dual_equiv_dual_apply -> Subspace.dualEquivDual_apply is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)), Eq.{succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualEquivDual._proof_4.{u1} K _inst_1)) (Submodule.module.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Subspace.dualEquivDual._proof_1.{u1} K _inst_1) (Subspace.dualEquivDual._proof_2.{u1} K _inst_1)) (Subspace.dualEquivDual.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.mk.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) x (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Iff.mpr (Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Exists.{succ (max u2 u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ))) (LinearMap.mem_range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualEquivDual._proof_3.{u1} K _inst_1) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) (Exists.intro.{succ (max u2 u1)} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) φ (rfl.{succ (max u2 u1)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) => (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (FunLike.hasCoeToFun.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddHomClass.toFunLike.{max u2 u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toHasAdd.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u2 u1, u1, u1, max u2 u1, max u2 u1} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1))) K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} K K (Module.Dual.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K (coeSort.{succ u2, succ (succ u2)} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) W) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_1.{u1} K _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Subspace.dualLift._proof_2.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)))))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {W : Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3} (φ : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) φ) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toZero.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddMonoid.toZero.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (Module.toDistribMulAction.{u1, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.toDistribMulAction.{u1, max u1 u2} K (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u1 u2, max u1 u2, max u1 u2} K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Subtype.{succ (max u1 u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Submodule.module.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Subspace.dualEquivDual.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Subtype.mk.{max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) x (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (Iff.mpr (Membership.mem.{max u1 u2, max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.setLike.{u1, max u1 u2} K (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ) (LinearMap.range.{u1, u1, max u1 u2, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W))) (Exists.{succ (max u1 u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u1 u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) y) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ))) (LinearMap.mem_range.{max u1 u2, max u1 u2, max u1 u2, u1, u1} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) (Exists.intro.{max (succ u1) (succ u2)} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (y : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Eq.{succ (max u1 u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) y) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) y) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)) φ (rfl.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) φ) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) => Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) _x) (AddHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (AddZeroClass.toAdd.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{max u1 u2} (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (SemilinearMapClass.toAddHomClass.{max u1 u2, u1, u1, max u1 u2, max u1 u2} (LinearMap.{u1, u1, max u2 u1, max u2 u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u2, max u1 u2} K K (Module.Dual.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} K V (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subspace.{u1, u2} K V (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x W)) K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 W) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommRing.toCommMonoid.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (Subspace.dualLift.{u1, u2} K V _inst_1 _inst_2 _inst_3 W) φ)))))
+Case conversion may be inaccurate. Consider using '#align subspace.dual_equiv_dual_apply Subspace.dualEquivDual_applyₓ'. -/
 @[simp]
 theorem dualEquivDual_apply (φ : Module.Dual K W) :
     W.dualEquivDual φ = ⟨W.dualLift φ, mem_range.2 ⟨φ, rfl⟩⟩ :=
@@ -1107,6 +1603,7 @@ instance [H : FiniteDimensional K V] : FiniteDimensional K (Module.Dual K V) :=
 
 variable [FiniteDimensional K V] [FiniteDimensional K V₁]
 
+#print Subspace.dualAnnihilator_dualAnnihilator_eq /-
 theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
     W.dualAnnihilator.dualAnnihilator = Module.mapEvalEquiv K V W :=
   by
@@ -1114,19 +1611,25 @@ theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
   rw [dual_coannihilator, ← Module.mapEvalEquiv_symm_apply] at this
   rwa [← OrderIso.symm_apply_eq]
 #align subspace.dual_annihilator_dual_annihilator_eq Subspace.dualAnnihilator_dualAnnihilator_eq
+-/
 
+#print Subspace.dual_finrank_eq /-
 -- TODO(kmill): https://github.com/leanprover-community/mathlib/pull/17521#discussion_r1083241963
 @[simp]
 theorem dual_finrank_eq : finrank K (Module.Dual K V) = finrank K V :=
   LinearEquiv.finrank_eq (Basis.ofVectorSpace K V).toDualEquiv.symm
 #align subspace.dual_finrank_eq Subspace.dual_finrank_eq
+-/
 
+#print Subspace.quotDualEquivAnnihilator /-
 /-- The quotient by the dual is isomorphic to its dual annihilator.  -/
 noncomputable def quotDualEquivAnnihilator (W : Subspace K V) :
     (Module.Dual K V ⧸ W.dualLift.range) ≃ₗ[K] W.dualAnnihilator :=
   LinearEquiv.quotEquivOfQuotEquiv <| LinearEquiv.trans W.quotAnnihilatorEquiv W.dualEquivDual
 #align subspace.quot_dual_equiv_annihilator Subspace.quotDualEquivAnnihilator
+-/
 
+#print Subspace.quotEquivAnnihilator /-
 /-- The quotient by a subspace is isomorphic to its dual annihilator. -/
 noncomputable def quotEquivAnnihilator (W : Subspace K V) : (V ⧸ W) ≃ₗ[K] W.dualAnnihilator :=
   by
@@ -1134,9 +1637,11 @@ noncomputable def quotEquivAnnihilator (W : Subspace K V) : (V ⧸ W) ≃ₗ[K]
   refine' linear_equiv.quot_equiv_of_equiv _ (Basis.ofVectorSpace K V).toDualEquiv
   exact (Basis.ofVectorSpace K W).toDualEquiv.trans W.dual_equiv_dual
 #align subspace.quot_equiv_annihilator Subspace.quotEquivAnnihilator
+-/
 
 open FiniteDimensional
 
+#print Subspace.finrank_dualCoannihilator_eq /-
 @[simp]
 theorem finrank_dualCoannihilator_eq {Φ : Subspace K (Module.Dual K V)} :
     finrank K Φ.dualCoannihilator = finrank K Φ.dualAnnihilator :=
@@ -1144,12 +1649,15 @@ theorem finrank_dualCoannihilator_eq {Φ : Subspace K (Module.Dual K V)} :
   rw [Submodule.dualCoannihilator, ← Module.evalEquiv_toLinearMap]
   exact LinearEquiv.finrank_eq (LinearEquiv.ofSubmodule' _ _)
 #align subspace.finrank_dual_coannihilator_eq Subspace.finrank_dualCoannihilator_eq
+-/
 
+#print Subspace.finrank_add_finrank_dualCoannihilator_eq /-
 theorem finrank_add_finrank_dualCoannihilator_eq (W : Subspace K (Module.Dual K V)) :
     finrank K W + finrank K W.dualCoannihilator = finrank K V := by
   rw [finrank_dual_coannihilator_eq, W.quot_equiv_annihilator.finrank_eq.symm, add_comm,
     Submodule.finrank_quotient_add_finrank, Subspace.dual_finrank_eq]
 #align subspace.finrank_add_finrank_dual_coannihilator_eq Subspace.finrank_add_finrank_dualCoannihilator_eq
+-/
 
 end
 
@@ -1165,6 +1673,7 @@ variable [AddCommMonoid M₁] [Module R M₁] [AddCommMonoid M₂] [Module R M
 
 variable (f : M₁ →ₗ[R] M₂)
 
+#print LinearMap.ker_dualMap_eq_dualAnnihilator_range /-
 theorem ker_dualMap_eq_dualAnnihilator_range : f.dualMap.ker = f.range.dualAnnihilator :=
   by
   ext φ; constructor <;> intro hφ
@@ -1177,7 +1686,14 @@ theorem ker_dualMap_eq_dualAnnihilator_range : f.dualMap.ker = f.range.dualAnnih
     rw [Submodule.mem_dualAnnihilator] at hφ
     exact hφ (f x) ⟨x, rfl⟩
 #align linear_map.ker_dual_map_eq_dual_annihilator_range LinearMap.ker_dualMap_eq_dualAnnihilator_range
+-/
 
+/- warning: linear_map.range_dual_map_le_dual_annihilator_ker -> LinearMap.range_dualMap_le_dualAnnihilator_ker is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5), LE.le.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (Preorder.toHasLe.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (Submodule.completeLattice.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))))))) (LinearMap.range.{u1, u1, max u3 u1, max u2 u1, max (max u3 u1) u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1))) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_1.{u1} R _inst_1)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} M₂] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5), LE.le.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Preorder.toLE.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (PartialOrder.toPreorder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (OmegaCompletePartialOrder.toPartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (CompleteLattice.instOmegaCompletePartialOrder.{max u1 u2} (Submodule.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Submodule.completeLattice.{u1, max u1 u2} R (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))))) (LinearMap.range.{u1, u1, max u1 u3, max u1 u2, max (max u1 u2) u3} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearMap.semilinearMapClass.{u1, u1, max u1 u3, max u1 u2} R R (Module.Dual.{u1, u3} R M₂ _inst_1 _inst_4 _inst_5) (Module.Dual.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R M₂ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M₁ R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.dualMap.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M₁ _inst_1 _inst_2 _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M₁ M₂ _inst_2 _inst_4 _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M₁ M₂ (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f))
+Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_le_dual_annihilator_ker LinearMap.range_dualMap_le_dualAnnihilator_kerₓ'. -/
 theorem range_dualMap_le_dualAnnihilator_ker : f.dualMap.range ≤ f.ker.dualAnnihilator :=
   by
   rintro _ ⟨ψ, rfl⟩
@@ -1196,6 +1712,7 @@ variable [CommRing R] [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R
 
 namespace Submodule
 
+#print Submodule.dualCopairing /-
 /-- Given a submodule, corestrict to the pairing on `M ⧸ W` by
 simultaneously restricting to `W.dual_annihilator`.
 
@@ -1208,13 +1725,21 @@ def dualCopairing (W : Submodule R M) : W.dualAnnihilator →ₗ[R] M ⧸ W →
         ext ⟨φ, hφ⟩
         exact (mem_dual_annihilator φ).mp hφ w hw)
 #align submodule.dual_copairing Submodule.dualCopairing
+-/
 
+/- warning: submodule.dual_copairing_apply -> Submodule.dualCopairing_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3} (φ : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1))) => (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.dualCopairing.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x)) (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) φ x)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3} (φ : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) φ) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (fun (_x : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.dualCopairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ x)
+Case conversion may be inaccurate. Consider using '#align submodule.dual_copairing_apply Submodule.dualCopairing_applyₓ'. -/
 @[simp]
 theorem dualCopairing_apply {W : Submodule R M} (φ : W.dualAnnihilator) (x : M) :
     W.dualCopairing φ (Quotient.mk x) = φ x :=
   rfl
 #align submodule.dual_copairing_apply Submodule.dualCopairing_apply
 
+#print Submodule.dualPairing /-
 /-- Given a submodule, restrict to the pairing on `W` by
 simultaneously corestricting to `module.dual R M ⧸ W.dual_annihilator`.
 This is `submodule.dual_restrict` factored through the quotient by its kernel (which
@@ -1224,13 +1749,26 @@ See `subspace.dual_pairing_nondegenerate`. -/
 def dualPairing (W : Submodule R M) : Module.Dual R M ⧸ W.dualAnnihilator →ₗ[R] W →ₗ[R] R :=
   W.dualAnnihilator.liftQ W.dualRestrict le_rfl
 #align submodule.dual_pairing Submodule.dualPairing
+-/
 
+/- warning: submodule.dual_pairing_apply -> Submodule.dualPairing_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3} (φ : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Module.Dual.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1))) => (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.hasQuotient.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualPairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualPairing._proof_2.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.dualPairing.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommRing.toRing.{u1} R _inst_1) (LinearMap.addCommGroup.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W) φ)) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) φ ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) W) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x W))))) x))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3} (φ : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.Quotient.mk.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) φ)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) (fun (_x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) (CommRing.toCommSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u2, u2, max (max u2 u1) u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (fun (_x : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) => LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u2 u1} (HasQuotient.Quotient.{max u1 u2, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.hasQuotient.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.Quotient.addCommGroup.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x W)) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.dualPairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (Submodule.Quotient.mk.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommRing.toRing.{u2} R _inst_1) (LinearMap.addCommGroup.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W) φ)) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) φ (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) W)) x))
+Case conversion may be inaccurate. Consider using '#align submodule.dual_pairing_apply Submodule.dualPairing_applyₓ'. -/
 @[simp]
 theorem dualPairing_apply {W : Submodule R M} (φ : Module.Dual R M) (x : W) :
     W.dualPairing (Quotient.mk φ) x = φ x :=
   rfl
 #align submodule.dual_pairing_apply Submodule.dualPairing_apply
 
+/- warning: submodule.range_dual_map_mkq_eq -> Submodule.range_dualMap_mkQ_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap.{u1, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Submodule.mkQ.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Eq.{max (succ u2) (succ u1)} (Submodule.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.range.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearMap.dualMap.{u2, u1, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Submodule.mkQ.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)
+Case conversion may be inaccurate. Consider using '#align submodule.range_dual_map_mkq_eq Submodule.range_dualMap_mkQ_eqₓ'. -/
 /-- That $\operatorname{im}(q^* : (V/W)^* \to V^*) = \operatorname{ann}(W)$. -/
 theorem range_dualMap_mkQ_eq (W : Submodule R M) : W.mkQ.dualMap.range = W.dualAnnihilator :=
   by
@@ -1246,6 +1784,7 @@ theorem range_dualMap_mkQ_eq (W : Submodule R M) : W.mkQ.dualMap.range = W.dualA
     rfl
 #align submodule.range_dual_map_mkq_eq Submodule.range_dualMap_mkQ_eq
 
+#print Submodule.dualQuotEquivDualAnnihilator /-
 /-- Equivalence $(M/W)^* \approx \operatorname{ann}(W)$. That is, there is a one-to-one
 correspondence between the dual of `M ⧸ W` and those elements of the dual of `M` that
 vanish on `W`.
@@ -1264,18 +1803,37 @@ def dualQuotEquivDualAnnihilator (W : Submodule R M) :
       ext
       rfl)
 #align submodule.dual_quot_equiv_dual_annihilator Submodule.dualQuotEquivDualAnnihilator
+-/
 
+/- warning: submodule.dual_quot_equiv_dual_annihilator_apply -> Submodule.dualQuotEquivDualAnnihilator_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (φ : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) => (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) -> (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1)) (Submodule.dualQuotEquivDualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) φ) x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) φ (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (φ : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) φ) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) => Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toZero.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toZero.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toAddZeroClass.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearEquiv.{u2, u2, max u1 u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) φ (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x))
+Case conversion may be inaccurate. Consider using '#align submodule.dual_quot_equiv_dual_annihilator_apply Submodule.dualQuotEquivDualAnnihilator_applyₓ'. -/
 @[simp]
 theorem dualQuotEquivDualAnnihilator_apply (W : Submodule R M) (φ : Module.Dual R (M ⧸ W)) (x : M) :
     dualQuotEquivDualAnnihilator W φ x = φ (Quotient.mk x) :=
   rfl
 #align submodule.dual_quot_equiv_dual_annihilator_apply Submodule.dualQuotEquivDualAnnihilator_apply
 
+/- warning: submodule.dual_copairing_eq -> Submodule.dualCopairing_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ (max u2 u1)} (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.{u1, u1, u2, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualCopairing._proof_1.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualCopairing._proof_2.{u1} R _inst_1))) (Submodule.dualCopairing.{u1, u2} R M _inst_1 _inst_2 _inst_3 W) (LinearEquiv.toLinearMap.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Eq.{max (succ u2) (succ u1)} (LinearMap.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (LinearMap.{u2, u2, u1, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.dualCopairing.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) (LinearEquiv.toLinearMap.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (LinearEquiv.symm.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W)))
+Case conversion may be inaccurate. Consider using '#align submodule.dual_copairing_eq Submodule.dualCopairing_eqₓ'. -/
 theorem dualCopairing_eq (W : Submodule R M) :
     W.dualCopairing = (dualQuotEquivDualAnnihilator W).symm.toLinearMap :=
   rfl
 #align submodule.dual_copairing_eq Submodule.dualCopairing_eq
 
+/- warning: submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk -> Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (W : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (φ : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (x : M), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (fun (_x : Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) => (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) -> R) (Module.Dual.hasCoeToFun.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1))) => (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) -> (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, max u2 u1, max u2 u1} R R (Module.Dual.{u1, u2} R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.addCommMonoid.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (LinearMap.module.{u1, u1, u1, u2, u1} R R R (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.Quotient.module.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_4.{u1} R _inst_1)) (Submodule.module.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator._proof_3.{u1} R _inst_1)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.dualQuotEquivDualAnnihilator._proof_1.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator._proof_2.{u1} R _inst_1) (Submodule.dualQuotEquivDualAnnihilator.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)) φ) (Submodule.Quotient.mk.{u1, u2} R M (CommRing.toRing.{u1} R _inst_1) _inst_2 _inst_3 W x)) (coeFn.{succ (max u2 u1), max (succ u2) (succ u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (fun (x : coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) => M -> R) (coeFnTrans.{max (succ u2) (succ u1), succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeBaseAux.{succ (max u2 u1), succ (max u2 u1)} (coeSort.{succ (max u2 u1), succ (succ (max u2 u1))} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) Type.{max u2 u1} (SetLike.hasCoeToSort.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W)) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeSubtype.{succ (max u2 u1)} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (x : Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => Membership.Mem.{max u2 u1, max u2 u1} (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.setLike.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.dualAnnihilator._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) x (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 W))))) φ x)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (W : Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (φ : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) φ) (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (fun (_x : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) => R) _x) (Module.Dual.instFunLikeDual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (fun (_x : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) => Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toZero.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddMonoid.toAddZeroClass.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toZero.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddMonoid.toAddZeroClass.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.toDistribMulAction.{u2, max u2 u1} R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (LinearEquiv.symm.{u2, u2, max u2 u1, max u2 u1} R R (Module.Dual.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.addCommMonoid.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3) W) (Submodule.Quotient.addCommGroup.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Submodule.Quotient.module.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.module.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.dualQuotEquivDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W)) φ) (Submodule.Quotient.mk.{u2, u1} R M (CommRing.toRing.{u2} R _inst_1) _inst_2 _inst_3 W x)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Subtype.{succ (max u2 u1)} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x : Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => Membership.mem.{max u2 u1, max u2 u1} (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u2, max u1 u2} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.setLike.{u2, max u2 u1} R (Module.Dual.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u2} R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} R R R M R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) _inst_3 (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (smulCommClass_self.{u2, u2} R R (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))))) x (Submodule.dualAnnihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 W))) M (fun (x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.10148 : M) => R) x) (Submodule.instFunLikeSubtypeDualToCommSemiringToAddCommMonoidMemSubmoduleToSemiringAddCommMonoidToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToModuleIdInstModuleLinearMapAddCommMonoidSmulCommClass_selfToCommMonoidToMulActionToMonoidWithZeroToZeroToCommMonoidWithZeroToMulActionWithZeroInstMembershipSetLikeDualAnnihilator.{u2, u1} R M _inst_1 _inst_2 _inst_3 W) φ x)
+Case conversion may be inaccurate. Consider using '#align submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk Submodule.dualQuotEquivDualAnnihilator_symm_apply_mkₓ'. -/
 @[simp]
 theorem dualQuotEquivDualAnnihilator_symm_apply_mk (W : Submodule R M) (φ : W.dualAnnihilator)
     (x : M) : (dualQuotEquivDualAnnihilator W).symm φ (Quotient.mk x) = φ x :=
@@ -1288,6 +1846,12 @@ namespace LinearMap
 
 open Submodule
 
+/- warning: linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective -> LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, max u3 u1, max u2 u1, max (max u3 u1) u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)))
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u3, max u3 u2} R (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.range.{u3, u3, max u3 u1, max u3 u2, max (max u3 u2) u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, max u1 u3, max u2 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u3, u3, max u3 u1, max u3 u2} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.dualMap.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)))
+Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjectiveₓ'. -/
 theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
     (hf : Function.Surjective f) : f.dualMap.range = f.ker.dualAnnihilator :=
   by
@@ -1304,6 +1868,12 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
       LinearMap.quotKerEquivRange_symm_apply_image, mkq_apply]
 #align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective
 
+/- warning: linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective -> LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {M' : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (coeFn.{succ (max u3 u1), succ (max u3 u1)} (LinearMap.{u1, u1, max u3 u1, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) -> (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)))) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u3 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (CommRing.toCommSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.dualMap.{u1, u3, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) M' (Submodule.addCommMonoid.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (Submodule.module.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.subtype.{u1, u3} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f))))) -> (Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.range.{u1, u1, max u3 u1, max u2 u1, max (max u3 u1) u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, max u3 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.semilinearMapClass.{u1, u1, max u3 u1, max u2 u1} R R (Module.Dual.{u1, u3} R M' (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R M' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_5 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _inst_3 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.dualMap.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)))
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u2}} {M' : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u3, u3, max u1 u3, max u1 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (fun (_x : Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) => Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u3 u1, max u3 u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u1} R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommRing.toCommSemiring.{u3} R _inst_1) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.dualMap.{u3, u1, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) (Subtype.{succ u1} M' (fun (x : M') => Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) M' (Submodule.setLike.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5)) x (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))) M' (Submodule.addCommMonoid.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (Submodule.module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (Submodule.subtype.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) f))))) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u3, max u3 u2} R (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.range.{u3, u3, max u3 u1, max u3 u2, max (max u3 u2) u1} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, max u1 u3, max u2 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (LinearMap.semilinearMapClass.{u3, u3, max u3 u1, max u3 u2} R R (Module.Dual.{u3, u1} R M' (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5) (Module.Dual.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R M' R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_5 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) _inst_3 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.dualMap.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_5 f)) (Submodule.dualAnnihilator.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (LinearMap.ker.{u3, u3, u2, u1, max u2 u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)))
+Case conversion may be inaccurate. Consider using '#align linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjectiveₓ'. -/
 -- Note, this can be specialized to the case where `R` is an injective `R`-module, or when
 -- `f.coker` is a projective `R`-module.
 theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M →ₗ[R] M')
@@ -1332,10 +1902,18 @@ variable [AddCommGroup V₁] [Module K V₁] [AddCommGroup V₂] [Module K V₂]
 
 namespace LinearMap
 
+#print LinearMap.dualPairing_nondegenerate /-
 theorem dualPairing_nondegenerate : (dualPairing K V₁).Nondegenerate :=
   ⟨separatingLeft_iff_ker_eq_bot.mpr ker_id, fun x => (forall_dual_apply_eq_zero_iff K x).mp⟩
 #align linear_map.dual_pairing_nondegenerate LinearMap.dualPairing_nondegenerate
+-/
 
+/- warning: linear_map.dual_map_surjective_of_injective -> LinearMap.dualMap_surjective_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) -> (Function.Surjective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f)))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f)) -> (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f)))
+Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_surjective_of_injective LinearMap.dualMap_surjective_of_injectiveₓ'. -/
 theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function.Injective f) :
     Function.Surjective f.dualMap := by
   intro φ
@@ -1348,12 +1926,20 @@ theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function
   exact LinearEquiv.symm_apply_apply f' x
 #align linear_map.dual_map_surjective_of_injective LinearMap.dualMap_surjective_of_injective
 
+#print LinearMap.range_dualMap_eq_dualAnnihilator_ker /-
 theorem range_dualMap_eq_dualAnnihilator_ker (f : V₁ →ₗ[K] V₂) :
     f.dualMap.range = f.ker.dualAnnihilator :=
   range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective f <|
     dualMap_surjective_of_injective (range f).injective_subtype
 #align linear_map.range_dual_map_eq_dual_annihilator_ker LinearMap.range_dualMap_eq_dualAnnihilator_ker
+-/
 
+/- warning: linear_map.dual_map_surjective_iff -> LinearMap.dualMap_surjective_iff is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Surjective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Injective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Injective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_surjective_iff LinearMap.dualMap_surjective_iffₓ'. -/
 /-- For vector spaces, `f.dual_map` is surjective if and only if `f` is injective -/
 @[simp]
 theorem dualMap_surjective_iff {f : V₁ →ₗ[K] V₂} :
@@ -1368,12 +1954,15 @@ namespace Subspace
 
 open Submodule
 
+#print Subspace.dualPairing_eq /-
 theorem dualPairing_eq (W : Subspace K V₁) : W.dualPairing = W.quotAnnihilatorEquiv.toLinearMap :=
   by
   ext
   rfl
 #align subspace.dual_pairing_eq Subspace.dualPairing_eq
+-/
 
+#print Subspace.dualPairing_nondegenerate /-
 theorem dualPairing_nondegenerate (W : Subspace K V₁) : W.dualPairing.Nondegenerate :=
   by
   constructor
@@ -1385,7 +1974,9 @@ theorem dualPairing_nondegenerate (W : Subspace K V₁) : W.dualPairing.Nondegen
     simpa only [Submodule.dualPairing_apply, dual_lift_of_subtype] using
       h (Submodule.Quotient.mk (W.dual_lift φ))
 #align subspace.dual_pairing_nondegenerate Subspace.dualPairing_nondegenerate
+-/
 
+#print Subspace.dualCopairing_nondegenerate /-
 theorem dualCopairing_nondegenerate (W : Subspace K V₁) : W.dualCopairing.Nondegenerate :=
   by
   constructor
@@ -1396,7 +1987,9 @@ theorem dualCopairing_nondegenerate (W : Subspace K V₁) : W.dualCopairing.Nond
     rw [← forall_mem_dual_annihilator_apply_eq_zero_iff, SetLike.forall]
     exact id
 #align subspace.dual_copairing_nondegenerate Subspace.dualCopairing_nondegenerate
+-/
 
+#print Subspace.dualAnnihilator_inf_eq /-
 -- Argument from https://math.stackexchange.com/a/2423263/172988
 theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
     (W ⊓ W').dualAnnihilator = W.dualAnnihilator ⊔ W'.dualAnnihilator :=
@@ -1415,7 +2008,14 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
   use a', a'.property, b', b'.property
   rfl
 #align subspace.dual_annihilator_inf_eq Subspace.dualAnnihilator_inf_eq
+-/
 
+/- warning: subspace.dual_annihilator_infi_eq -> Subspace.dualAnnihilator_iInf_eq is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] {ι : Type.{u3}} [_inst_6 : Finite.{succ u3} ι] (W : ι -> (Subspace.{u1, u2} K V₁ (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3)), Eq.{succ (max u2 u1)} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.dualAnnihilator.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (iInf.{u2, succ u3} (Subspace.{u1, u2} K V₁ (Field.toDivisionRing.{u1} K _inst_1) _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) ι (fun (i : ι) => W i))) (iSup.{max u2 u1, succ u3} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (ConditionallyCompleteLattice.toHasSup.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (Submodule.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.completeLattice.{u1, max u2 u1} K (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.dualAnnihilator._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (W i)))
+but is expected to have type
+  forall {K : Type.{u2}} [_inst_1 : Field.{u2} K] {V₁ : Type.{u3}} [_inst_2 : AddCommGroup.{u3} V₁] [_inst_3 : Module.{u2, u3} K V₁ (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2)] {ι : Type.{u1}} [_inst_6 : Finite.{succ u1} ι] (W : ι -> (Subspace.{u2, u3} K V₁ (Field.toDivisionRing.{u2} K _inst_1) _inst_2 _inst_3)), Eq.{max (succ u2) (succ u3)} (Submodule.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))) (Submodule.dualAnnihilator.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3 (iInf.{u3, succ u1} (Subspace.{u2, u3} K V₁ (Field.toDivisionRing.{u2} K _inst_1) _inst_2 _inst_3) (Submodule.instInfSetSubmodule.{u2, u3} K V₁ (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K (Field.toDivisionRing.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) ι (fun (i : ι) => W i))) (iSup.{max u2 u3, succ u1} (Submodule.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u2, max u3 u2} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))) (Submodule.completeLattice.{u2, max u2 u3} K (Module.Dual.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (LinearMap.addCommMonoid.{u2, u2, u3, u2} K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} K K K V₁ K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (Semiring.toModule.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (smulCommClass_self.{u2, u2} K K (CommSemiring.toCommMonoid.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} K K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (CommMonoidWithZero.toZero.{u2} K (CommSemiring.toCommMonoidWithZero.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))))))))) ι (fun (i : ι) => Submodule.dualAnnihilator.{u2, u3} K V₁ (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2) _inst_3 (W i)))
+Case conversion may be inaccurate. Consider using '#align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_iInf_eqₓ'. -/
 -- This is also true if `V₁` is finite dimensional since one can restrict `ι` to some subtype
 -- for which the infi and supr are the same.
 --
@@ -1436,6 +2036,7 @@ theorem dualAnnihilator_iInf_eq {ι : Type _} [Finite ι] (W : ι → Subspace K
     rw [iInf_option, iSup_option, dual_annihilator_inf_eq, h]
 #align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_iInf_eq
 
+#print Subspace.isCompl_dualAnnihilator /-
 /-- For vector spaces, dual annihilators carry direct sum decompositions
 to direct sum decompositions. -/
 theorem isCompl_dualAnnihilator {W W' : Subspace K V₁} (h : IsCompl W W') :
@@ -1446,13 +2047,16 @@ theorem isCompl_dualAnnihilator {W W' : Subspace K V₁} (h : IsCompl W W') :
     dual_annihilator_bot]
   exact ⟨rfl, rfl⟩
 #align subspace.is_compl_dual_annihilator Subspace.isCompl_dualAnnihilator
+-/
 
+#print Subspace.dualQuotDistrib /-
 /-- For finite-dimensional vector spaces, one can distribute duals over quotients by identifying
 `W.dual_lift.range` with `W`. Note that this depends on a choice of splitting of `V₁`. -/
 def dualQuotDistrib [FiniteDimensional K V₁] (W : Subspace K V₁) :
     Module.Dual K (V₁ ⧸ W) ≃ₗ[K] Module.Dual K V₁ ⧸ W.dualLift.range :=
   W.dualQuotEquivDualAnnihilator.trans W.quotDualEquivAnnihilator.symm
 #align subspace.dual_quot_distrib Subspace.dualQuotDistrib
+-/
 
 end Subspace
 
@@ -1464,6 +2068,7 @@ variable [FiniteDimensional K V₂]
 
 namespace LinearMap
 
+#print LinearMap.finrank_range_dualMap_eq_finrank_range /-
 -- TODO(kmill) remove finite_dimensional if possible
 -- see https://github.com/leanprover-community/mathlib/pull/17521#discussion_r1083242551
 @[simp]
@@ -1478,7 +2083,14 @@ theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
   change _ + _ = _ + _
   rw [finrank_range_add_finrank_ker f.dual_map, add_comm, this]
 #align linear_map.finrank_range_dual_map_eq_finrank_range LinearMap.finrank_range_dualMap_eq_finrank_range
+-/
 
+/- warning: linear_map.dual_map_injective_iff -> LinearMap.dualMap_injective_iff is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Injective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Surjective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Surjective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iffₓ'. -/
 /-- `f.dual_map` is injective if and only if `f` is surjective -/
 @[simp]
 theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
@@ -1494,6 +2106,12 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
     Subspace.dual_finrank_eq]
 #align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iff
 
+/- warning: linear_map.dual_map_bijective_iff -> LinearMap.dualMap_bijective_iff is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Bijective.{max (succ u3) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (coeFn.{max (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u3 u1)) (succ (max u2 u1))} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) => (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) -> (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3)) (LinearMap.hasCoeToFun.{u1, u1, max u3 u1, max u2 u1} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.module.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_1.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearMap.dualMap._proof_2.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Bijective.{succ u2, succ u3} V₁ V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f))
+but is expected to have type
+  forall {K : Type.{u1}} [_inst_1 : Field.{u1} K] {V₁ : Type.{u2}} {V₂ : Type.{u3}} [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddCommGroup.{u3} V₂] [_inst_5 : Module.{u1, u3} K V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4)] [_inst_6 : FiniteDimensional.{u1, u3} K V₂ (Field.toDivisionRing.{u1} K _inst_1) _inst_4 _inst_5] {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5}, Iff (Function.Bijective.{max (succ u1) (succ u3), max (succ u1) (succ u2)} (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u3 u1, max u2 u1} K K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (fun (_x : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) => Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u3, max u1 u2} K K (Module.Dual.{u1, u3} K V₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5) (Module.Dual.{u1, u2} K V₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u1} K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} K K K V₂ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_5 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} K K K V₁ K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Semiring.toModule.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (smulCommClass_self.{u1, u1} K K (CommSemiring.toCommMonoid.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} K K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (CommMonoidWithZero.toZero.{u1} K (CommSemiring.toCommMonoidWithZero.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.dualMap.{u1, u2, u3} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_5 f))) (Function.Bijective.{succ u2, succ u3} V₁ V₂ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V₂ _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) f))
+Case conversion may be inaccurate. Consider using '#align linear_map.dual_map_bijective_iff LinearMap.dualMap_bijective_iffₓ'. -/
 /-- `f.dual_map` is bijective if and only if `f` is -/
 @[simp]
 theorem dualMap_bijective_iff {f : V₁ →ₗ[K] V₂} :
@@ -1533,6 +2151,7 @@ variable [CommSemiring R] [AddCommMonoid M] [AddCommMonoid N]
 
 variable [Module R M] [Module R N]
 
+#print TensorProduct.dualDistrib /-
 /-- The canonical linear map from `dual M ⊗ dual N` to `dual (M ⊗ N)`,
 sending `f ⊗ g` to the composition of `tensor_product.map f g` with
 the natural isomorphism `R ⊗ R ≃ R`.
@@ -1540,9 +2159,16 @@ the natural isomorphism `R ⊗ R ≃ R`.
 def dualDistrib : Dual R M ⊗[R] Dual R N →ₗ[R] Dual R (M ⊗[R] N) :=
   compRight ↑(TensorProduct.lid R R) ∘ₗ homTensorHomMap R M N R R
 #align tensor_product.dual_distrib TensorProduct.dualDistrib
+-/
 
 variable {R M N}
 
+/- warning: tensor_product.dual_distrib_apply -> TensorProduct.dualDistrib_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_5 : CommSemiring.{u1} R] [_inst_6 : AddCommMonoid.{u2} M] [_inst_7 : AddCommMonoid.{u3} N] [_inst_8 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6] [_inst_9 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7] (f : Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (g : Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (m : M) (n : N), Eq.{succ u1} R (coeFn.{max (succ (max u2 u3)) (succ u1), max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (fun (_x : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) => (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (coeFn.{max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1)), max (succ (max (max u2 u1) u3 u1)) (succ (max (max u2 u3) u1))} (LinearMap.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5))) (fun (_x : LinearMap.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5))) => (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) -> (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9))) (LinearMap.hasCoeToFun.{u1, u1, max (max u2 u1) u3 u1, max (max u2 u3) u1} R R (TensorProduct.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.module.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_3.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (TensorProduct.dualDistrib.{u1, u2, u3} R M N _inst_5 _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.tmul.{u1, max u2 u1, max u3 u1} R _inst_5 (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R _inst_5) (CommSemiring.toSemiring.{u1} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))) (CommSemiring.toSemiring.{u1} R _inst_5) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)) (TensorProduct.dualDistrib._proof_2.{u1} R _inst_5)) f g)) (TensorProduct.tmul.{u1, u2, u3} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) (fun (_x : Module.Dual.{u1, u2} R M _inst_5 _inst_6 _inst_8) => M -> R) (Module.Dual.hasCoeToFun.{u1, u2} R M _inst_5 _inst_6 _inst_8) f m) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) (fun (_x : Module.Dual.{u1, u3} R N _inst_5 _inst_7 _inst_9) => N -> R) (Module.Dual.hasCoeToFun.{u1, u3} R N _inst_5 _inst_7 _inst_9) g n))
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_5 : CommSemiring.{u3} R] [_inst_6 : AddCommMonoid.{u2} M] [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6] [_inst_9 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7] (f : Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (g : Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (m : M) (n : N), Eq.{succ u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => R) (TensorProduct.tmul.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.tmul.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) f g)) (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (fun (_x : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) => R) _x) (Module.Dual.instFunLikeDual.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u3, u3, max (max u1 u3) u2 u3, max (max u1 u2) u3} R R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (TensorProduct.addCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.addCommMonoid.{u3, u3, max u2 u1, u3} R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u2 u1, u3} R R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (fun (_x : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) => Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max (max u3 u2) u1, max (max u3 u2) u1} R R (TensorProduct.{u3, max u2 u3, max u1 u3} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (Module.Dual.{u3, max u1 u2} R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) _inst_5 (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9)) (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.addCommMonoid.{u3, u3, max u2 u1, u3} R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u2 u1, u3} R R R (TensorProduct.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) (TensorProduct.addCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (TensorProduct.dualDistrib.{u3, u2, u1} R M N _inst_5 _inst_6 _inst_7 _inst_8 _inst_9) (TensorProduct.tmul.{u3, max u3 u2, max u3 u1} R _inst_5 (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) (LinearMap.addCommMonoid.{u3, u3, u2, u3} R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.addCommMonoid.{u3, u3, u1, u3} R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u3} R R R M R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_8 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} R R R N R (CommSemiring.toSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R _inst_5) _inst_7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))) _inst_9 (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5))) (CommSemiring.toSemiring.{u3} R _inst_5) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R _inst_5) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_5)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_5)))))) f g)) (TensorProduct.tmul.{u3, u2, u1} R _inst_5 M N _inst_6 _inst_7 _inst_8 _inst_9 m n)) (HMul.hMul.{u3, u3, u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : N) => R) n) ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (instHMul.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) (CommSemiring.toSemiring.{u3} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) m) _inst_5))))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (Module.Dual.{u3, u2} R M _inst_5 _inst_6 _inst_8) M (fun (_x : M) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : M) => R) _x) (Module.Dual.instFunLikeDual.{u3, u2} R M _inst_5 _inst_6 _inst_8) f m) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (Module.Dual.{u3, u1} R N _inst_5 _inst_7 _inst_9) N (fun (_x : N) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : N) => R) _x) (Module.Dual.instFunLikeDual.{u3, u1} R N _inst_5 _inst_7 _inst_9) g n))
+Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_apply TensorProduct.dualDistrib_applyₓ'. -/
 @[simp]
 theorem dualDistrib_apply (f : Dual R M) (g : Dual R N) (m : M) (n : N) :
     dualDistrib R M N (f ⊗ₜ g) (m ⊗ₜ n) = f m * g n :=
@@ -1557,6 +2183,12 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N]
 
 variable [Module R M] [Module R N]
 
+/- warning: tensor_product.dual_distrib_inv_of_basis -> TensorProduct.dualDistribInvOfBasis is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {ι : Type.{u4}} {κ : Type.{u5}} [_inst_1 : DecidableEq.{succ u4} ι] [_inst_2 : DecidableEq.{succ u5} κ] [_inst_3 : Fintype.{u4} ι] [_inst_4 : Fintype.{u5} κ] [_inst_5 : CommRing.{u1} R] [_inst_6 : AddCommGroup.{u2} M] [_inst_7 : AddCommGroup.{u3} N] [_inst_8 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6)] [_inst_9 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7)], (Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) -> (Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) -> (LinearMap.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {ι : Type.{u4}} {κ : Type.{u5}} [_inst_1 : DecidableEq.{succ u4} ι] [_inst_2 : DecidableEq.{succ u5} κ] [_inst_3 : Fintype.{u4} ι] [_inst_4 : Fintype.{u5} κ] [_inst_5 : CommRing.{u1} R] [_inst_6 : AddCommGroup.{u2} M] [_inst_7 : AddCommGroup.{u3} N] [_inst_8 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6)] [_inst_9 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7)], (Basis.{u4, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) -> (Basis.{u5, u1, u3} κ R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) -> (LinearMap.{u1, u1, max (max u3 u2) u1, max (max u3 u1) u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Module.Dual.{u1, max u3 u2} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u1 u2, max u1 u3} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, max u1 u2, max u1 u3} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R _inst_5) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))))))))
+Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_inv_of_basis TensorProduct.dualDistribInvOfBasisₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /-- An inverse to `dual_tensor_dual_map` given bases.
 -/
@@ -1567,6 +2199,12 @@ noncomputable def dualDistribInvOfBasis (b : Basis ι R M) (c : Basis κ R N) :
       applyₗ (c j) ∘ₗ applyₗ (b i) ∘ₗ lcurry R M N R
 #align tensor_product.dual_distrib_inv_of_basis TensorProduct.dualDistribInvOfBasis
 
+/- warning: tensor_product.dual_distrib_inv_of_basis_apply -> TensorProduct.dualDistribInvOfBasis_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {ι : Type.{u4}} {κ : Type.{u5}} [_inst_1 : DecidableEq.{succ u4} ι] [_inst_2 : DecidableEq.{succ u5} κ] [_inst_3 : Fintype.{u4} ι] [_inst_4 : Fintype.{u5} κ] [_inst_5 : CommRing.{u1} R] [_inst_6 : AddCommGroup.{u2} M] [_inst_7 : AddCommGroup.{u3} N] [_inst_8 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6)] [_inst_9 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7)] (b : Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (c : Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (f : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)), Eq.{succ (max (max u2 u1) u3 u1)} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (coeFn.{max (succ (max (max u2 u3) u1)) (succ (max (max u2 u1) u3 u1)), max (succ (max (max u2 u3) u1)) (succ (max (max u2 u1) u3 u1))} (LinearMap.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) (fun (_x : LinearMap.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) => (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) -> (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)))) (LinearMap.hasCoeToFun.{u1, u1, max (max u2 u3) u1, max (max u2 u1) u3 u1} R R (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, max u2 u3, u1} R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (LinearMap.module.{u1, u1, u1, max u2 u3, u1} R R R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_3.{u1} R _inst_5)) (TensorProduct.module.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (TensorProduct.dualDistribInvOfBasis.{u1, u2, u3, u4, u5} R M N ι κ (fun (a : ι) (b : ι) => _inst_1 a b) (fun (a : κ) (b : κ) => _inst_2 a b) _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 b c) f) (Finset.sum.{max (max u2 u1) u3 u1, u4} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) ι (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Finset.univ.{u4} ι _inst_3) (fun (i : ι) => Finset.sum.{max (max u2 u1) u3 u1, u5} (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) κ (TensorProduct.addCommMonoid.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (Finset.univ.{u5} κ _inst_4) (fun (j : κ) => SMul.smul.{u1, max (max u2 u1) u3 u1} R (TensorProduct.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (TensorProduct.hasSmul.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5))) (coeFn.{max (succ (max u2 u3)) (succ u1), max (succ (max u2 u3)) (succ u1)} (Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) (fun (_x : Module.Dual.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) => (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) -> R) (Module.Dual.hasCoeToFun.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u1} R _inst_5) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9)) f (TensorProduct.tmul.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_8 _inst_9 (coeFn.{max (succ u4) (succ u1) (succ u2), max (succ u4) (succ u2)} (Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (fun (_x : Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) => ι -> M) (FunLike.hasCoeToFun.{max (succ u4) (succ u1) (succ u2), succ u4, succ u2} (Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) ι (fun (_x : ι) => M) (Basis.funLike.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8)) b i) (coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (fun (_x : Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) => κ -> N) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) κ (fun (_x : κ) => N) (Basis.funLike.{u5, u1, u3} κ R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9)) c j))) (TensorProduct.tmul.{u1, max u2 u1, max u3 u1} R (CommRing.toCommSemiring.{u1} R _inst_5) (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_1.{u1} R _inst_5)) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (TensorProduct.dualDistribInvOfBasis._proof_2.{u1} R _inst_5)) (coeFn.{max (succ u4) (succ u1) (succ (max u2 u1)), max (succ u4) (succ (max u2 u1))} (Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) (fun (_x : Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) => ι -> (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8)) (FunLike.hasCoeToFun.{max (succ u4) (succ u1) (succ (max u2 u1)), succ u4, succ (max u2 u1)} (Basis.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) ι (fun (_x : ι) => Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Basis.funLike.{u4, u1, max u2 u1} ι R (Module.Dual.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) _inst_8) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u2, u1} R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u2, u1} R R R M R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_8 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5)))) (Basis.dualBasis.{u1, u2, u4} R M ι _inst_5 _inst_6 _inst_8 (fun (a : ι) (b : ι) => _inst_1 a b) b (Finite.of_fintype.{u4} ι _inst_3)) i) (coeFn.{max (succ u5) (succ u1) (succ (max u3 u1)), max (succ u5) (succ (max u3 u1))} (Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) (fun (_x : Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) => κ -> (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9)) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ (max u3 u1)), succ u5, succ (max u3 u1)} (Basis.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5))) κ (fun (_x : κ) => Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Basis.funLike.{u5, u1, max u3 u1} κ R (Module.Dual.{u1, u3} R N (CommRing.toCommSemiring.{u1} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) _inst_9) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (LinearMap.addCommMonoid.{u1, u1, u3, u1} R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) (LinearMap.module.{u1, u1, u1, u3, u1} R R R N R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) _inst_9 (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Basis.dualBasis._proof_1.{u1} R _inst_5)))) (Basis.dualBasis.{u1, u3, u5} R N κ _inst_5 _inst_7 _inst_9 (fun (a : κ) (b : κ) => _inst_2 a b) c (Finite.of_fintype.{u5} κ _inst_4)) j)))))
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {ι : Type.{u5}} {κ : Type.{u2}} [_inst_1 : DecidableEq.{succ u5} ι] [_inst_2 : DecidableEq.{succ u2} κ] [_inst_3 : Fintype.{u5} ι] [_inst_4 : Fintype.{u2} κ] [_inst_5 : CommRing.{u4} R] [_inst_6 : AddCommGroup.{u3} M] [_inst_7 : AddCommGroup.{u1} N] [_inst_8 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6)] [_inst_9 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7)] (b : Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (c : Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (f : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)), Eq.{max (max (succ u4) (succ u3)) (succ u1)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (max (succ u4) (succ u3)) (succ u1), max (max (succ u4) (succ u3)) (succ u1)} (LinearMap.{u4, u4, max (max u1 u3) u4, max (max u1 u4) u3 u4} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u4} R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u4} R R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))))) (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (fun (_x : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, max (max u4 u3) u1, max (max u4 u3) u1} R R (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, max u3 u1, u4} R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, max u3 u1, u4} R R R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (TensorProduct.dualDistribInvOfBasis.{u4, u3, u1, u5, u2} R M N ι κ (fun (a : ι) (b : ι) => _inst_1 a b) (fun (a : κ) (b : κ) => _inst_2 a b) _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 b c) f) (Finset.sum.{max (max u4 u3) u1, u5} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) ι (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Finset.univ.{u5} ι _inst_3) (fun (i : ι) => Finset.sum.{max (max u4 u3) u1, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) κ (TensorProduct.addCommMonoid.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Finset.univ.{u2} κ _inst_4) (fun (j : κ) => HSMul.hSMul.{u4, max (max u4 u1) u4 u3, max (max u4 u3) u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5)))))) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) => TensorProduct.{u4, max u3 u4, max u1 u4} R (CommRing.toCommSemiring.{u4} R _inst_5) (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) f) (instHSMul.{u4, max (max u4 u3) u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5)))))) (TensorProduct.instSMulTensorProduct.{u4, max u4 u3, max u4 u1} ((fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (a : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) a) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u4} (Module.Dual.{u4, max u1 u3} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (fun (_x : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => (fun (x._@.Mathlib.LinearAlgebra.Dual._hyg.172 : TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) => R) _x) (Module.Dual.instFunLikeDual.{u4, max u3 u1} R (TensorProduct.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (CommRing.toCommSemiring.{u4} R _inst_5) (TensorProduct.addCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9)) f (TensorProduct.tmul.{u4, u3, u1} R (CommRing.toCommSemiring.{u4} R _inst_5) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_8 _inst_9 (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) b i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, succ u1} (Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) κ (fun (_x : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => N) _x) (Basis.funLike.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) c j))) (TensorProduct.tmul.{u4, max u4 u3, max u4 u1} R (CommRing.toCommSemiring.{u4} R _inst_5) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) i) ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) j) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} R (NonAssocRing.toNonUnitalNonAssocRing.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (Monoid.toMulAction.{u4} R (CommMonoid.toMonoid.{u4} R (CommRing.toCommMonoid.{u4} R _inst_5))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, max (succ u4) (succ u3)} (Basis.{u5, u4, max u3 u4} ι R (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) _x) (Basis.funLike.{u5, u4, max u4 u3} ι R (Module.Dual.{u4, u3} R M (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) _inst_8) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u3, u4} R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u4} R R R M R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_8 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Basis.dualBasis.{u4, u3, u5} R M ι _inst_5 _inst_6 _inst_8 (fun (a : ι) (b : ι) => _inst_1 a b) b (Finite.of_fintype.{u5} ι _inst_3)) i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u2, max (succ u4) (succ u1)} (Basis.{u2, u4, max u1 u4} κ R (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) κ (fun (_x : κ) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ) => Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) _x) (Basis.funLike.{u2, u4, max u4 u1} κ R (Module.Dual.{u4, u1} R N (CommRing.toCommSemiring.{u4} R _inst_5) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) _inst_9) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (LinearMap.addCommMonoid.{u4, u4, u1, u4} R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u4} R R R N R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u1} N _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))))) _inst_9 (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (smulCommClass_self.{u4, u4} R R (CommRing.toCommMonoid.{u4} R _inst_5) (MulActionWithZero.toMulAction.{u4, u4} R R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (CommMonoidWithZero.toZero.{u4} R (CommSemiring.toCommMonoidWithZero.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))) (MonoidWithZero.toMulActionWithZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)))))))) (Basis.dualBasis.{u4, u1, u2} R N κ _inst_5 _inst_7 _inst_9 (fun (a : κ) (b : κ) => _inst_2 a b) c (Finite.of_fintype.{u2} κ _inst_4)) j)))))
+Case conversion may be inaccurate. Consider using '#align tensor_product.dual_distrib_inv_of_basis_apply TensorProduct.dualDistribInvOfBasis_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem dualDistribInvOfBasis_apply (b : Basis ι R M) (c : Basis κ R N) (f : Dual R (M ⊗[R] N)) :
@@ -1574,6 +2212,7 @@ theorem dualDistribInvOfBasis_apply (b : Basis ι R M) (c : Basis κ R N) (f : D
   simp [dual_distrib_inv_of_basis]
 #align tensor_product.dual_distrib_inv_of_basis_apply TensorProduct.dualDistribInvOfBasis_apply
 
+#print TensorProduct.dualDistribEquivOfBasis /-
 /-- A linear equivalence between `dual M ⊗ dual N` and `dual (M ⊗ N)` given bases for `M` and `N`.
 It sends `f ⊗ g` to the composition of `tensor_product.map f g` with the natural
 isomorphism `R ⊗ R ≃ R`.
@@ -1594,6 +2233,7 @@ noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N)
       dual_distrib_apply, ← smul_tmul_smul, ← tmul_sum, ← sum_tmul, Basis.coe_dualBasis,
       Basis.sum_dual_apply_smul_coord]
 #align tensor_product.dual_distrib_equiv_of_basis TensorProduct.dualDistribEquivOfBasis
+-/
 
 variable (R M N)
 
@@ -1603,6 +2243,7 @@ variable [Nontrivial R]
 
 open Classical
 
+#print TensorProduct.dualDistribEquiv /-
 /--
 A linear equivalence between `dual M ⊗ dual N` and `dual (M ⊗ N)` when `M` and `N` are finite free
 modules. It sends `f ⊗ g` to the composition of `tensor_product.map f g` with the natural
@@ -1612,6 +2253,7 @@ isomorphism `R ⊗ R ≃ R`.
 noncomputable def dualDistribEquiv : Dual R M ⊗[R] Dual R N ≃ₗ[R] Dual R (M ⊗[R] N) :=
   dualDistribEquivOfBasis (Module.Free.chooseBasis R M) (Module.Free.chooseBasis R N)
 #align tensor_product.dual_distrib_equiv TensorProduct.dualDistribEquiv
+-/
 
 end TensorProduct
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -911,15 +911,15 @@ theorem dualCoannihilator_sup_eq (U V : Submodule R (Module.Dual R M)) :
   (dualAnnihilator_gc R M).u_inf
 #align submodule.dual_coannihilator_sup_eq Submodule.dualCoannihilator_sup_eq
 
-theorem dualAnnihilator_supᵢ_eq {ι : Type _} (U : ι → Submodule R M) :
+theorem dualAnnihilator_iSup_eq {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, U i).dualAnnihilator = ⨅ i : ι, (U i).dualAnnihilator :=
-  (dualAnnihilator_gc R M).l_supᵢ
-#align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_supᵢ_eq
+  (dualAnnihilator_gc R M).l_iSup
+#align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eq
 
-theorem dualCoannihilator_supᵢ_eq {ι : Type _} (U : ι → Submodule R (Module.Dual R M)) :
+theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.Dual R M)) :
     (⨆ i : ι, U i).dualCoannihilator = ⨅ i : ι, (U i).dualCoannihilator :=
-  (dualAnnihilator_gc R M).u_infᵢ
-#align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_supᵢ_eq
+  (dualAnnihilator_gc R M).u_iInf
+#align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
 
 /-- See also `subspace.dual_annihilator_inf_eq` for vector subspaces. -/
 theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
@@ -930,13 +930,13 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
 
 /-- See also `subspace.dual_annihilator_infi_eq` for vector subspaces when `ι` is finite. -/
-theorem supᵢ_dualAnnihilator_le_infᵢ {ι : Type _} (U : ι → Submodule R M) :
+theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
     (⨆ i : ι, (U i).dualAnnihilator) ≤ (⨅ i : ι, U i).dualAnnihilator :=
   by
   rw [le_dual_annihilator_iff_le_dual_coannihilator, dual_coannihilator_supr_eq]
-  apply infᵢ_mono
+  apply iInf_mono
   exact fun i : ι => le_dual_annihilator_dual_coannihilator (U i)
-#align submodule.supr_dual_annihilator_le_infi Submodule.supᵢ_dualAnnihilator_le_infᵢ
+#align submodule.supr_dual_annihilator_le_infi Submodule.iSup_dualAnnihilator_le_iInf
 
 end Submodule
 
@@ -1423,7 +1423,7 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
 -- for `module.dual R (Π (i : ι), V ⧸ W i) ≃ₗ[K] Π (i : ι), module.dual R (V ⧸ W i)`, which is not
 -- true for infinite `ι`. One would need to add additional hypothesis on `W` (for example, it might
 -- be true when the family is inf-closed).
-theorem dualAnnihilator_infᵢ_eq {ι : Type _} [Finite ι] (W : ι → Subspace K V₁) :
+theorem dualAnnihilator_iInf_eq {ι : Type _} [Finite ι] (W : ι → Subspace K V₁) :
     (⨅ i : ι, W i).dualAnnihilator = ⨆ i : ι, (W i).dualAnnihilator :=
   by
   revert ι
@@ -1431,10 +1431,10 @@ theorem dualAnnihilator_infᵢ_eq {ι : Type _} [Finite ι] (W : ι → Subspace
   · intro α β h hyp W
     rw [← h.infi_comp, hyp (W ∘ h), ← h.supr_comp]
   · intro W
-    rw [supᵢ_of_empty', infᵢ_of_empty', infₛ_empty, supₛ_empty, dual_annihilator_top]
+    rw [iSup_of_empty', iInf_of_empty', sInf_empty, sSup_empty, dual_annihilator_top]
   · intro α _ h W
-    rw [infᵢ_option, supᵢ_option, dual_annihilator_inf_eq, h]
-#align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_infᵢ_eq
+    rw [iInf_option, iSup_option, dual_annihilator_inf_eq, h]
+#align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_iInf_eq
 
 /-- For vector spaces, dual annihilators carry direct sum decompositions
 to direct sum decompositions. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
 
 ! This file was ported from Lean 3 source module linear_algebra.dual
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit b1c017582e9f18d8494e5c18602a8cb4a6f843ac
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -100,20 +100,12 @@ variable (R : Type _) (M : Type _)
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M]
 
-/- ./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler module[module] R -/
 /-- The dual space of an R-module M is the R-module of linear maps `M → R`. -/
+@[reducible]
 def Dual :=
-  M →ₗ[R] R deriving AddCommMonoid,
-  «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler module[module] R»
+  M →ₗ[R] R
 #align module.dual Module.Dual
 
-instance {S : Type _} [CommRing S] {N : Type _} [AddCommGroup N] [Module S N] :
-    AddCommGroup (Dual S N) :=
-  LinearMap.addCommGroup
-
-instance : LinearMapClass (Dual R M) R M R :=
-  LinearMap.semilinearMapClass
-
 /-- The canonical pairing of a vector space and its algebraic dual. -/
 def dualPairing (R M) [CommSemiring R] [AddCommMonoid M] [Module R M] :
     Module.Dual R M →ₗ[R] M →ₗ[R] R :=
@@ -408,11 +400,16 @@ section Finite
 variable [Finite ι]
 
 /-- A vector space is linearly equivalent to its dual space. -/
-@[simps]
 def toDualEquiv : M ≃ₗ[R] Dual R M :=
   LinearEquiv.ofBijective b.toDual ⟨ker_eq_bot.mp b.toDual_ker, range_eq_top.mp b.toDual_range⟩
 #align basis.to_dual_equiv Basis.toDualEquiv
 
+-- `simps` times out when generating this
+@[simp]
+theorem toDualEquiv_apply (m : M) : b.toDualEquiv m = b.toDual m :=
+  rfl
+#align basis.to_dual_equiv_apply Basis.toDualEquiv_apply
+
 /-- Maps a basis for `V` to a basis for the dual space. -/
 def dualBasis : Basis ι R (Dual R M) :=
   b.map b.toDualEquiv

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
 
 ! This file was ported from Lean 3 source module linear_algebra.dual
-! leanprover-community/mathlib commit 5455cb0b5f3be8f8b22c55366fbc6e380dbff579
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -519,15 +519,15 @@ theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b :
   rw [← coe_dual_basis, total_dual_basis]
 #align basis.total_coord Basis.total_coord
 
-theorem dual_dim_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
+theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
     Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) := by
   classical
     cases nonempty_fintype ι
-    have := LinearEquiv.lift_dim_eq b.to_dual_equiv
+    have := LinearEquiv.lift_rank_eq b.to_dual_equiv
     simp only [Cardinal.lift_umax] at this
     rw [this, ← Cardinal.lift_umax]
     apply Cardinal.lift_id
-#align basis.dual_dim_eq Basis.dual_dim_eq
+#align basis.dual_rank_eq Basis.dual_rank_eq
 
 end Basis
 
@@ -585,10 +585,10 @@ theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v
 end
 
 -- TODO(jmc): generalize to rings, once `module.rank` is generalized
-theorem dual_dim_eq [FiniteDimensional K V] :
+theorem dual_rank_eq [FiniteDimensional K V] :
     Cardinal.lift (Module.rank K V) = Module.rank K (Dual K V) :=
-  (Basis.ofVectorSpace K V).dual_dim_eq
-#align module.dual_dim_eq Module.dual_dim_eq
+  (Basis.ofVectorSpace K V).dual_rank_eq
+#align module.dual_rank_eq Module.dual_rank_eq
 
 theorem erange_coe [FiniteDimensional K V] : (eval K V).range = ⊤ :=
   letI : IsNoetherian K V := IsNoetherian.iff_fg.2 inferInstance

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -734,7 +734,7 @@ theorem lc_coeffs (m : M) : DualBases.lc e (h.coeffs m) = m :=
 /-- `(h : dual_bases e ε).basis` shows the family of vectors `e` forms a basis. -/
 @[simps]
 def basis : Basis ι R M :=
-  Basis.of_repr
+  Basis.ofRepr
     { toFun := coeffs h
       invFun := lc e
       left_inv := lc_coeffs h

mathlib commit https://github.com/leanprover-community/mathlib/commit/dd6388c44e6f6b4547070b887c5905d5cfe6c9f8

@@ -1335,9 +1335,9 @@ variable [AddCommGroup V₁] [Module K V₁] [AddCommGroup V₂] [Module K V₂]
 
 namespace LinearMap
 
-theorem dualPairingNondegenerate : (dualPairing K V₁).Nondegenerate :=
+theorem dualPairing_nondegenerate : (dualPairing K V₁).Nondegenerate :=
   ⟨separatingLeft_iff_ker_eq_bot.mpr ker_id, fun x => (forall_dual_apply_eq_zero_iff K x).mp⟩
-#align linear_map.dual_pairing_nondegenerate LinearMap.dualPairingNondegenerate
+#align linear_map.dual_pairing_nondegenerate LinearMap.dualPairing_nondegenerate
 
 theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function.Injective f) :
     Function.Surjective f.dualMap := by
@@ -1377,7 +1377,7 @@ theorem dualPairing_eq (W : Subspace K V₁) : W.dualPairing = W.quotAnnihilator
   rfl
 #align subspace.dual_pairing_eq Subspace.dualPairing_eq
 
-theorem dualPairingNondegenerate (W : Subspace K V₁) : W.dualPairing.Nondegenerate :=
+theorem dualPairing_nondegenerate (W : Subspace K V₁) : W.dualPairing.Nondegenerate :=
   by
   constructor
   · rw [LinearMap.separatingLeft_iff_ker_eq_bot, dual_pairing_eq]
@@ -1387,9 +1387,9 @@ theorem dualPairingNondegenerate (W : Subspace K V₁) : W.dualPairing.Nondegene
     intro φ
     simpa only [Submodule.dualPairing_apply, dual_lift_of_subtype] using
       h (Submodule.Quotient.mk (W.dual_lift φ))
-#align subspace.dual_pairing_nondegenerate Subspace.dualPairingNondegenerate
+#align subspace.dual_pairing_nondegenerate Subspace.dualPairing_nondegenerate
 
-theorem dualCopairingNondegenerate (W : Subspace K V₁) : W.dualCopairing.Nondegenerate :=
+theorem dualCopairing_nondegenerate (W : Subspace K V₁) : W.dualCopairing.Nondegenerate :=
   by
   constructor
   · rw [LinearMap.separatingLeft_iff_ker_eq_bot, dual_copairing_eq]
@@ -1398,7 +1398,7 @@ theorem dualCopairingNondegenerate (W : Subspace K V₁) : W.dualCopairing.Nonde
     simp only [quotient.quot_mk_eq_mk, dual_copairing_apply, quotient.mk_eq_zero]
     rw [← forall_mem_dual_annihilator_apply_eq_zero_iff, SetLike.forall]
     exact id
-#align subspace.dual_copairing_nondegenerate Subspace.dualCopairingNondegenerate
+#align subspace.dual_copairing_nondegenerate Subspace.dualCopairing_nondegenerate
 
 -- Argument from https://math.stackexchange.com/a/2423263/172988
 theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -641,7 +641,7 @@ variable {R M ι : Type _}
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 -- TODO: In Lean 4 we can remove this and use `by { intros; exact Set.toFinite _ }` as a default
 -- argument.
 /-- Try using `set.to_finite` to dispatch a `set.finite` goal. -/
@@ -649,7 +649,7 @@ unsafe def use_finite_instance : tactic Unit :=
   sorry
 #align use_finite_instance use_finite_instance
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic use_finite_instance -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic use_finite_instance -/
 /-- `e` and `ε` have characteristic properties of a basis and its dual -/
 @[nolint has_nonempty_instance]
 structure Module.DualBases (e : ι → M) (ε : ι → Dual R M) : Prop where

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -498,9 +498,9 @@ open Classical
 
 variable [Finite R M] [Free R M] [Nontrivial R]
 
-instance dualFree : Free R (Dual R M) :=
-  Free.ofBasis (Free.chooseBasis R M).dualBasis
-#align basis.dual_free Basis.dualFree
+instance dual_free : Free R (Dual R M) :=
+  Free.of_basis (Free.chooseBasis R M).dualBasis
+#align basis.dual_free Basis.dual_free
 
 instance dual_finite : Finite R (Dual R M) :=
   Finite.of_basis (Free.chooseBasis R M).dualBasis

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

This breaks a few simp proofs which were expecting these lemmas to apply to the data binders but not the prop binders.

@@ -1012,12 +1012,12 @@ theorem dualCoannihilator_sup_eq (U V : Submodule R (Module.Dual R M)) :
   (dualAnnihilator_gc R M).u_inf
 #align submodule.dual_coannihilator_sup_eq Submodule.dualCoannihilator_sup_eq
 
-theorem dualAnnihilator_iSup_eq {ι : Type*} (U : ι → Submodule R M) :
+theorem dualAnnihilator_iSup_eq {ι : Sort*} (U : ι → Submodule R M) :
     (⨆ i : ι, U i).dualAnnihilator = ⨅ i : ι, (U i).dualAnnihilator :=
   (dualAnnihilator_gc R M).l_iSup
 #align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eq
 
-theorem dualCoannihilator_iSup_eq {ι : Type*} (U : ι → Submodule R (Module.Dual R M)) :
+theorem dualCoannihilator_iSup_eq {ι : Sort*} (U : ι → Submodule R (Module.Dual R M)) :
     (⨆ i : ι, U i).dualCoannihilator = ⨅ i : ι, (U i).dualCoannihilator :=
   (dualAnnihilator_gc R M).u_iInf
 #align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
@@ -1030,7 +1030,7 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
 
 /-- See also `Subspace.dualAnnihilator_iInf_eq` for vector subspaces when `ι` is finite. -/
-theorem iSup_dualAnnihilator_le_iInf {ι : Type*} (U : ι → Submodule R M) :
+theorem iSup_dualAnnihilator_le_iInf {ι : Sort*} (U : ι → Submodule R M) :
     ⨆ i : ι, (U i).dualAnnihilator ≤ (⨅ i : ι, U i).dualAnnihilator := by
   rw [le_dualAnnihilator_iff_le_dualCoannihilator, dualCoannihilator_iSup_eq]
   apply iInf_mono
@@ -1571,6 +1571,7 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
 -- for `Module.Dual R (Π (i : ι), V ⧸ W i) ≃ₗ[K] Π (i : ι), Module.Dual R (V ⧸ W i)`, which is not
 -- true for infinite `ι`. One would need to add additional hypothesis on `W` (for example, it might
 -- be true when the family is inf-closed).
+-- TODO: generalize to `Sort`
 theorem dualAnnihilator_iInf_eq {ι : Type*} [Finite ι] (W : ι → Subspace K V₁) :
     (⨅ i : ι, W i).dualAnnihilator = ⨆ i : ι, (W i).dualAnnihilator := by
   revert ι

We define the coroots of a finite-dimensional semisimple Lie algebra with coefficients in a field characteristic zero and establish the key property that a coroot is complementary to the kernel of the root.

In addition we carry out some related, light refactoring. The most important points are:

• Promote LieModule.weight from a subtype to a structure LieModule.Weight + expand its API (we need this expanded API for the headline results).
• Replace the definition LieAlgebra.rootSpaceProductNegSelf with its range which we call LieAlgebra.corootSpace (in all places where we used this definition, it was the range that we actually used).
• Drop the very old (unused) definitions LieAlgebra.IsRoot and LieModule.IsWeight.

@@ -1453,6 +1453,36 @@ universe uK uV₁ uV₂
 variable {K : Type uK} [Field K] {V₁ : Type uV₁} {V₂ : Type uV₂}
 variable [AddCommGroup V₁] [Module K V₁] [AddCommGroup V₂] [Module K V₂]
 
+namespace Module.Dual
+
+variable [FiniteDimensional K V₁] {f : Module.Dual K V₁} (hf : f ≠ 0)
+
+open FiniteDimensional
+
+lemma range_eq_top_of_ne_zero :
+    LinearMap.range f = ⊤ := by
+  obtain ⟨v, hv⟩ : ∃ v, f v ≠ 0 := by contrapose! hf; ext v; simpa using hf v
+  rw [eq_top_iff]
+  exact fun x _ ↦ ⟨x • (f v)⁻¹ • v, by simp [inv_mul_cancel hv]⟩
+
+lemma finrank_ker_add_one_of_ne_zero :
+    finrank K (LinearMap.ker f) + 1 = finrank K V₁ := by
+  suffices finrank K (LinearMap.range f) = 1 by
+    rw [← (LinearMap.ker f).finrank_quotient_add_finrank, add_comm, add_left_inj,
+    f.quotKerEquivRange.finrank_eq, this]
+  rw [range_eq_top_of_ne_zero hf, finrank_top, finrank_self]
+
+lemma isCompl_ker_of_disjoint_of_ne_bot {p : Submodule K V₁}
+    (hpf : Disjoint (LinearMap.ker f) p) (hp : p ≠ ⊥) :
+    IsCompl (LinearMap.ker f) p := by
+  refine ⟨hpf, codisjoint_iff.mpr <| eq_of_le_of_finrank_le le_top ?_⟩
+  have : finrank K ↑(LinearMap.ker f ⊔ p) = finrank K (LinearMap.ker f) + finrank K p := by
+    simp [← Submodule.finrank_sup_add_finrank_inf_eq (LinearMap.ker f) p, hpf.eq_bot]
+  rwa [finrank_top, this, ← finrank_ker_add_one_of_ne_zero hf, add_le_add_iff_left,
+    Submodule.one_le_finrank_iff]
+
+end Module.Dual
+
 namespace LinearMap
 
 theorem dualPairing_nondegenerate : (dualPairing K V₁).Nondegenerate :=

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

@@ -751,7 +751,7 @@ def evalUseFiniteInstance : TacticM Unit := do
 elab "use_finite_instance" : tactic => evalUseFiniteInstance
 
 /-- `e` and `ε` have characteristic properties of a basis and its dual -/
--- @[nolint has_nonempty_instance] Porting note (#10927): removed
+-- @[nolint has_nonempty_instance] Porting note (#5171): removed
 structure Module.DualBases (e : ι → M) (ε : ι → Dual R M) : Prop where
   eval : ∀ i j : ι, ε i (e j) = if i = j then 1 else 0
   protected total : ∀ {m : M}, (∀ i, ε i m = 0) → m = 0

@@ -662,7 +662,7 @@ def evalEquiv : M ≃ₗ[R] Dual R (Dual R M) :=
 
 /-- The dual of a reflexive module is reflexive. -/
 instance Dual.instIsReflecive : IsReflexive R (Dual R M) :=
-⟨by simpa only [← symm_dualMap_evalEquiv] using (evalEquiv R M).dualMap.symm.bijective⟩
+  ⟨by simpa only [← symm_dualMap_evalEquiv] using (evalEquiv R M).dualMap.symm.bijective⟩
 
 /-- The isomorphism `Module.evalEquiv` induces an order isomorphism on subspaces. -/
 def mapEvalEquiv : Submodule R M ≃o Submodule R (Dual R (Dual R M)) :=

I removed some redundant instance arguments throughout Mathlib. To do this, I used VS Code's regex search. See https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/repeating.20instances.20from.20variable.20command I closed the previous PR for this and reopened it.

@@ -694,7 +694,7 @@ instance _root_.Prod.instModuleIsReflexive [IsReflexive R N] :
     exact Bijective.Prod_map (bijective_dual_eval R M) (bijective_dual_eval R N)
 
 variable {R M N} in
-lemma equiv [IsReflexive R M] (e : M ≃ₗ[R] N) : IsReflexive R N where
+lemma equiv (e : M ≃ₗ[R] N) : IsReflexive R N where
   bijective_dual_eval' := by
     let ed : Dual R (Dual R N) ≃ₗ[R] Dual R (Dual R M) := e.symm.dualMap.dualMap
     have : Dual.eval R N = ed.symm.comp ((Dual.eval R M).comp e.symm.toLinearMap) := by

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -101,7 +101,6 @@ namespace Module
 universe uR uA uM uM' uM''
 
 variable (R : Type uR) (A : Type uA) (M : Type uM)
-
 variable [CommSemiring R] [AddCommMonoid M] [Module R M]
 
 /-- The dual space of an R-module M is the R-module of linear maps `M → R`. -/
@@ -187,7 +186,6 @@ open Module
 universe u v v'
 
 variable {R : Type u} [CommSemiring R] {M₁ : Type v} {M₂ : Type v'}
-
 variable [AddCommMonoid M₁] [Module R M₁] [AddCommMonoid M₂] [Module R M₂]
 
 /-- Given a linear map `f : M₁ →ₗ[R] M₂`, `f.dualMap` is the linear map between the dual of
@@ -297,7 +295,6 @@ variable {R : Type uR} {M : Type uM} {K : Type uK} {V : Type uV} {ι : Type uι}
 section CommSemiring
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
-
 variable (b : Basis ι R M)
 
 /-- The linear map from a vector space equipped with basis to its dual vector space,
@@ -388,7 +385,6 @@ end CommSemiring
 section
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M] [Fintype ι]
-
 variable (b : Basis ι R M)
 
 @[simp]
@@ -404,7 +400,6 @@ end
 section CommRing
 
 variable [CommRing R] [AddCommGroup M] [Module R M] [DecidableEq ι]
-
 variable (b : Basis ι R M)
 
 section Finite
@@ -534,7 +529,6 @@ namespace Module
 
 universe uK uV
 variable {K : Type uK} {V : Type uV}
-
 variable [CommRing K] [AddCommGroup V] [Module K V] [Module.Free K V]
 
 open Module Module.Dual Submodule LinearMap Cardinal Basis FiniteDimensional
@@ -746,7 +740,6 @@ section DualBases
 open Module
 
 variable {R M ι : Type*}
-
 variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
 
 -- Porting note: replace use_finite_instance tactic
@@ -773,9 +766,7 @@ namespace Module.DualBases
 open Module Module.Dual LinearMap Function
 
 variable {R M ι : Type*}
-
 variable [CommRing R] [AddCommGroup M] [Module R M]
-
 variable {e : ι → M} {ε : ι → Dual R M}
 
 /-- The coefficients of `v` on the basis `e` -/
@@ -878,7 +869,6 @@ namespace Submodule
 universe u v w
 
 variable {R : Type u} {M : Type v} [CommSemiring R] [AddCommMonoid M] [Module R M]
-
 variable {W : Submodule R M}
 
 /-- The `dualRestrict` of a submodule `W` of `M` is the linear map from the
@@ -1263,9 +1253,7 @@ namespace LinearMap
 
 universe uR uM₁ uM₂
 variable {R : Type uR} [CommSemiring R] {M₁ : Type uM₁} {M₂ : Type uM₂}
-
 variable [AddCommMonoid M₁] [Module R M₁] [AddCommMonoid M₂] [Module R M₂]
-
 variable (f : M₁ →ₗ[R] M₂)
 
 -- Porting note (#11036): broken dot notation lean4#1910 LinearMap.ker
@@ -1291,7 +1279,6 @@ end LinearMap
 section CommRing
 
 variable {R M M' : Type*}
-
 variable [CommRing R] [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M']
 
 namespace Submodule
@@ -1464,7 +1451,6 @@ section VectorSpace
 -- Porting note: adding `uK` to avoid timeouts in `dualPairing_eq`
 universe uK uV₁ uV₂
 variable {K : Type uK} [Field K] {V₁ : Type uV₁} {V₂ : Type uV₂}
-
 variable [AddCommGroup V₁] [Module K V₁] [AddCommGroup V₂] [Module K V₂]
 
 namespace LinearMap
@@ -1728,11 +1714,8 @@ end VectorSpace
 namespace TensorProduct
 
 variable (R A : Type*) (M : Type*) (N : Type*)
-
 variable {ι κ : Type*}
-
 variable [DecidableEq ι] [DecidableEq κ]
-
 variable [Fintype ι] [Fintype κ]
 
 open BigOperators
@@ -1748,7 +1731,6 @@ open LinearMap
 section
 
 variable [CommSemiring R] [AddCommMonoid M] [AddCommMonoid N]
-
 variable [Module R M] [Module R N]
 
 /-- The canonical linear map from `Dual M ⊗ Dual N` to `Dual (M ⊗ N)`,
@@ -1771,7 +1753,6 @@ end
 
 namespace AlgebraTensorModule
 variable [CommSemiring R] [CommSemiring A] [Algebra R A] [AddCommMonoid M] [AddCommMonoid N]
-
 variable [Module R M] [Module A M] [Module R N] [IsScalarTower R A M]
 
 /-- Heterobasic version of `TensorProduct.dualDistrib` -/
@@ -1788,9 +1769,7 @@ theorem dualDistrib_apply (f : Dual A M) (g : Dual R N) (m : M) (n : N) :
 end AlgebraTensorModule
 
 variable {R M N}
-
 variable [CommRing R] [AddCommGroup M] [AddCommGroup N]
-
 variable [Module R M] [Module R N]
 
 /-- An inverse to `TensorProduct.dualDistrib` given bases.
@@ -1848,7 +1827,6 @@ noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N)
 #align tensor_product.dual_distrib_equiv_of_basis TensorProduct.dualDistribEquivOfBasis
 
 variable (R M N)
-
 variable [Module.Finite R M] [Module.Finite R N] [Module.Free R M] [Module.Free R N]
 
 /--

Move:

• Mathlib/Algebra/Module/DirectLimitAndTensorProduct.lean to LinearAlgebra/TensorProduct/DirectLimit.lean
• Mathlib/LinearAlgebra/TensorProduct to Mathlib/LinearAlgebra.TensorProduct.Basic.lean
• Mathlib/RingTheory/TensorProduct to Mathlib/RingTheory/TensorProduct/Basic.lean.

This follows suggestions 1, 2, 3 of

https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Tensor.20Products.20of.20modules.20and.20rings/near/424605543

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>

@@ -9,7 +9,7 @@ import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathlib.LinearAlgebra.Projection
 import Mathlib.LinearAlgebra.SesquilinearForm
-import Mathlib.RingTheory.TensorProduct
+import Mathlib.RingTheory.TensorProduct.Basic
 
 #align_import linear_algebra.dual from "leanprover-community/mathlib"@"b1c017582e9f18d8494e5c18602a8cb4a6f843ac"
 

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -1273,7 +1273,7 @@ theorem ker_dualMap_eq_dualAnnihilator_range :
     LinearMap.ker f.dualMap = f.range.dualAnnihilator := by
   ext
   simp_rw [mem_ker, ext_iff, Submodule.mem_dualAnnihilator,
-    ← SetLike.mem_coe, range_coe, Set.forall_range_iff]
+    ← SetLike.mem_coe, range_coe, Set.forall_mem_range]
   rfl
 #align linear_map.ker_dual_map_eq_dual_annihilator_range LinearMap.ker_dualMap_eq_dualAnnihilator_range
 

Fix two typos:

• In LinearAlgebra/Dual, the doctring of TensorProduct.dualDistribInvOfBasis says "An inverse to dual_tensor_dual_map given bases.", but dual_tensor_dual_map is now called TensorProduct.dualDistrib.
• In Algebra/Module/LinearMap/End, the doctstring of LinearMap.smulRight says "When f is an R-linear map taking values in S, then fun ↦ b, f b • x is an R-linear map.". The map should be fun b ↦ f b • x.

@@ -1793,7 +1793,7 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N]
 
 variable [Module R M] [Module R N]
 
-/-- An inverse to `dual_tensor_dual_map` given bases.
+/-- An inverse to `TensorProduct.dualDistrib` given bases.
 -/
 noncomputable def dualDistribInvOfBasis (b : Basis ι R M) (c : Basis κ R N) :
     Dual R (M ⊗[R] N) →ₗ[R] Dual R M ⊗[R] Dual R N :=

Classifies by adding issue number #11036 to porting notes claiming:

broken dot notation

@@ -369,12 +369,12 @@ theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   b.toDual_injective (by rwa [_root_.map_zero])
 #align basis.to_dual_inj Basis.toDual_inj
 
--- Porting note: broken dot notation lean4#1910 LinearMap.ker
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.ker
 theorem toDual_ker : LinearMap.ker b.toDual = ⊥ :=
   ker_eq_bot'.mpr b.toDual_inj
 #align basis.to_dual_ker Basis.toDual_ker
 
--- Porting note: broken dot notation lean4#1910 LinearMap.range
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 theorem toDual_range [Finite ι] : LinearMap.range b.toDual = ⊤ := by
   refine' eq_top_iff'.2 fun f => _
   let lin_comb : ι →₀ R := Finsupp.equivFunOnFinite.symm fun i => f (b i)
@@ -491,7 +491,7 @@ theorem eval_ker {ι : Type*} (b : Basis ι R M) :
   exact (Basis.forall_coord_eq_zero_iff _).mp fun i => hm (b.coord i)
 #align basis.eval_ker Basis.eval_ker
 
--- Porting note: broken dot notation lean4#1910 LinearMap.range
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 theorem eval_range {ι : Type*} [Finite ι] (b : Basis ι R M) :
     LinearMap.range (Dual.eval R M) = ⊤ := by
   classical
@@ -543,7 +543,7 @@ section
 
 variable (K) (V)
 
--- Porting note: broken dot notation lean4#1910 LinearMap.ker
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.ker
 theorem eval_ker : LinearMap.ker (eval K V) = ⊥ := by
   classical exact (Module.Free.chooseBasis K V).eval_ker
 #align module.eval_ker Module.eval_ker
@@ -619,7 +619,7 @@ theorem dual_rank_eq [Module.Finite K V] :
   (Module.Free.chooseBasis K V).dual_rank_eq
 #align module.dual_rank_eq Module.dual_rank_eq
 
--- Porting note: broken dot notation lean4#1910 LinearMap.range
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 theorem erange_coe [Module.Finite K V] : LinearMap.range (eval K V) = ⊤ :=
   (Module.Free.chooseBasis K V).eval_range
 #align module.erange_coe Module.erange_coe
@@ -902,7 +902,7 @@ theorem dualRestrict_apply (W : Submodule R M) (φ : Module.Dual R M) (x : W) :
   that `φ w = 0` for all `w ∈ W`. -/
 def dualAnnihilator {R : Type u} {M : Type v} [CommSemiring R] [AddCommMonoid M] [Module R M]
     (W : Submodule R M) : Submodule R <| Module.Dual R M :=
--- Porting note: broken dot notation lean4#1910 LinearMap.ker
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.ker
   LinearMap.ker W.dualRestrict
 #align submodule.dual_annihilator Submodule.dualAnnihilator
 
@@ -916,7 +916,7 @@ theorem mem_dualAnnihilator (φ : Module.Dual R M) : φ ∈ W.dualAnnihilator 
 /-- That $\operatorname{ker}(\iota^* : V^* \to W^*) = \operatorname{ann}(W)$.
 This is the definition of the dual annihilator of the submodule $W$. -/
 theorem dualRestrict_ker_eq_dualAnnihilator (W : Submodule R M) :
-    -- Porting note: broken dot notation lean4#1910 LinearMap.ker
+    -- Porting note (#11036): broken dot notation lean4#1910 LinearMap.ker
     LinearMap.ker W.dualRestrict = W.dualAnnihilator :=
   rfl
 #align submodule.dual_restrict_ker_eq_dual_annihilator Submodule.dualRestrict_ker_eq_dualAnnihilator
@@ -1171,7 +1171,7 @@ theorem quotAnnihilatorEquiv_apply (W : Subspace K V) (φ : Module.Dual K V) :
 #align subspace.quot_annihilator_equiv_apply Subspace.quotAnnihilatorEquiv_apply
 
 /-- The natural isomorphism from the dual of a subspace `W` to `W.dualLift.range`. -/
--- Porting note: broken dot notation lean4#1910 LinearMap.range
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 noncomputable def dualEquivDual (W : Subspace K V) :
     Module.Dual K W ≃ₗ[K] LinearMap.range W.dualLift :=
   LinearEquiv.ofInjective _ dualLift_injective
@@ -1216,7 +1216,7 @@ theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
 #align subspace.dual_annihilator_dual_annihilator_eq Subspace.dualAnnihilator_dualAnnihilator_eq
 
 /-- The quotient by the dual is isomorphic to its dual annihilator.  -/
--- Porting note: broken dot notation lean4#1910 LinearMap.range
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 noncomputable def quotDualEquivAnnihilator (W : Subspace K V) :
     (Module.Dual K V ⧸ LinearMap.range W.dualLift) ≃ₗ[K] W.dualAnnihilator :=
   LinearEquiv.quotEquivOfQuotEquiv <| LinearEquiv.trans W.quotAnnihilatorEquiv W.dualEquivDual
@@ -1268,7 +1268,7 @@ variable [AddCommMonoid M₁] [Module R M₁] [AddCommMonoid M₂] [Module R M
 
 variable (f : M₁ →ₗ[R] M₂)
 
--- Porting note: broken dot notation lean4#1910 LinearMap.ker
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.ker
 theorem ker_dualMap_eq_dualAnnihilator_range :
     LinearMap.ker f.dualMap = f.range.dualAnnihilator := by
   ext
@@ -1277,7 +1277,7 @@ theorem ker_dualMap_eq_dualAnnihilator_range :
   rfl
 #align linear_map.ker_dual_map_eq_dual_annihilator_range LinearMap.ker_dualMap_eq_dualAnnihilator_range
 
--- Porting note: broken dot notation lean4#1910 LinearMap.range
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 theorem range_dualMap_le_dualAnnihilator_ker :
     LinearMap.range f.dualMap ≤ f.ker.dualAnnihilator := by
   rintro _ ⟨ψ, rfl⟩
@@ -1339,7 +1339,7 @@ theorem dualPairing_apply {W : Submodule R M} (φ : Module.Dual R M) (x : W) :
   rfl
 #align submodule.dual_pairing_apply Submodule.dualPairing_apply
 
--- Porting note: broken dot notation lean4#1910 LinearMap.range
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 /-- That $\operatorname{im}(q^* : (V/W)^* \to V^*) = \operatorname{ann}(W)$. -/
 theorem range_dualMap_mkQ_eq (W : Submodule R M) :
     LinearMap.range W.mkQ.dualMap = W.dualAnnihilator := by
@@ -1362,7 +1362,7 @@ def dualQuotEquivDualAnnihilator (W : Submodule R M) :
     Module.Dual R (M ⧸ W) ≃ₗ[R] W.dualAnnihilator :=
   LinearEquiv.ofLinear
     (W.mkQ.dualMap.codRestrict W.dualAnnihilator fun φ =>
--- Porting note: broken dot notation lean4#1910 LinearMap.mem_range_self
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.mem_range_self
       W.range_dualMap_mkQ_eq ▸ LinearMap.mem_range_self W.mkQ.dualMap φ)
     W.dualCopairing (by ext; rfl) (by ext; rfl)
 #align submodule.dual_quot_equiv_dual_annihilator Submodule.dualQuotEquivDualAnnihilator
@@ -1421,7 +1421,7 @@ namespace LinearMap
 
 open Submodule
 
--- Porting note: broken dot notation lean4#1910 LinearMap.range
+-- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
     (hf : Function.Surjective f) : LinearMap.range f.dualMap = f.ker.dualAnnihilator :=
   ((f.quotKerEquivOfSurjective hf).dualMap.range_comp _).trans f.ker.range_dualMap_mkQ_eq
@@ -1436,7 +1436,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M
     rw [← range_eq_top, range_rangeRestrict]
   have := range_dualMap_eq_dualAnnihilator_ker_of_surjective f.rangeRestrict rr_surj
   convert this using 1
-  -- Porting note: broken dot notation lean4#1910
+  -- Porting note (#11036): broken dot notation lean4#1910
   · calc
       _ = range ((range f).subtype.comp f.rangeRestrict).dualMap := by simp
       _ = _ := ?_
@@ -1479,7 +1479,7 @@ theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function
   ⟨φ.comp f', ext fun x ↦ congr(φ <| $hf' x)⟩
 #align linear_map.dual_map_surjective_of_injective LinearMap.dualMap_surjective_of_injective
 
-  -- Porting note: broken dot notation lean4#1910 LinearMap.range
+  -- Porting note (#11036): broken dot notation lean4#1910 LinearMap.range
 theorem range_dualMap_eq_dualAnnihilator_ker (f : V₁ →ₗ[K] V₂) :
     LinearMap.range f.dualMap = f.ker.dualAnnihilator :=
   range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective f <|
@@ -1535,7 +1535,7 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
     (W ⊓ W').dualAnnihilator = W.dualAnnihilator ⊔ W'.dualAnnihilator := by
   refine' le_antisymm _ (sup_dualAnnihilator_le_inf W W')
   let F : V₁ →ₗ[K] (V₁ ⧸ W) × V₁ ⧸ W' := (Submodule.mkQ W).prod (Submodule.mkQ W')
-  -- Porting note: broken dot notation lean4#1910 LinearMap.ker
+  -- Porting note (#11036): broken dot notation lean4#1910 LinearMap.ker
   have : LinearMap.ker F = W ⊓ W' := by simp only [F, LinearMap.ker_prod, ker_mkQ]
   rw [← this, ← LinearMap.range_dualMap_eq_dualAnnihilator_ker]
   intro φ
@@ -1594,7 +1594,7 @@ namespace LinearMap
 
 @[simp]
 theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
-    -- Porting note: broken dot notation lean4#1910
+    -- Porting note (#11036): broken dot notation lean4#1910
     finrank K (LinearMap.range f.dualMap) = finrank K (LinearMap.range f) := by
   rw [congr_arg dualMap (show f = (range f).subtype.comp f.rangeRestrict by rfl),
     ← dualMap_comp_dualMap, range_comp,

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -694,7 +694,7 @@ instance _root_.Prod.instModuleIsReflexive [IsReflexive R N] :
       (dualProdDualEquivDual R M N).dualMap.trans
         (dualProdDualEquivDual R (Dual R M) (Dual R N)).symm
     have : Dual.eval R (M × N) = e.symm.comp ((Dual.eval R M).prodMap (Dual.eval R N)) := by
-      ext m f <;> simp
+      ext m f <;> simp [e]
     simp only [this, LinearEquiv.trans_symm, LinearEquiv.symm_symm, LinearEquiv.dualMap_symm,
       coe_comp, LinearEquiv.coe_coe, EquivLike.comp_bijective]
     exact Bijective.Prod_map (bijective_dual_eval R M) (bijective_dual_eval R N)
@@ -1536,7 +1536,7 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
   refine' le_antisymm _ (sup_dualAnnihilator_le_inf W W')
   let F : V₁ →ₗ[K] (V₁ ⧸ W) × V₁ ⧸ W' := (Submodule.mkQ W).prod (Submodule.mkQ W')
   -- Porting note: broken dot notation lean4#1910 LinearMap.ker
-  have : LinearMap.ker F = W ⊓ W' := by simp only [LinearMap.ker_prod, ker_mkQ]
+  have : LinearMap.ker F = W ⊓ W' := by simp only [F, LinearMap.ker_prod, ker_mkQ]
   rw [← this, ← LinearMap.range_dualMap_eq_dualAnnihilator_ker]
   intro φ
   rw [LinearMap.mem_range]

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

@@ -758,7 +758,7 @@ def evalUseFiniteInstance : TacticM Unit := do
 elab "use_finite_instance" : tactic => evalUseFiniteInstance
 
 /-- `e` and `ε` have characteristic properties of a basis and its dual -/
--- @[nolint has_nonempty_instance] Porting note: removed
+-- @[nolint has_nonempty_instance] Porting note (#10927): removed
 structure Module.DualBases (e : ι → M) (ε : ι → Dual R M) : Prop where
   eval : ∀ i j : ι, ε i (e j) = if i = j then 1 else 0
   protected total : ∀ {m : M}, (∀ i, ε i m = 0) → m = 0

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

@@ -843,7 +843,7 @@ def basis : Basis ι R M :=
         exact (ε i).map_smul c v }
 #align module.dual_bases.basis Module.DualBases.basis
 
--- Porting note : from simpNF the LHS simplifies; it yields lc_def.symm
+-- Porting note: from simpNF the LHS simplifies; it yields lc_def.symm
 -- probably not a useful simp lemma; nolint simpNF since it cannot see this removal
 attribute [-simp, nolint simpNF] basis_repr_symm_apply
 

@@ -197,6 +197,8 @@ def LinearMap.dualMap (f : M₁ →ₗ[R] M₂) : Dual R M₂ →ₗ[R] Dual R M
   Module.Dual.transpose (R := R) f
 #align linear_map.dual_map LinearMap.dualMap
 
+lemma LinearMap.dualMap_eq_lcomp (f : M₁ →ₗ[R] M₂) : f.dualMap = f.lcomp R := rfl
+
 -- Porting note: with reducible def need to specify some parameters to transpose explicitly
 theorem LinearMap.dualMap_def (f : M₁ →ₗ[R] M₂) : f.dualMap = Module.Dual.transpose (R := R) f :=
   rfl
@@ -264,6 +266,21 @@ theorem LinearEquiv.dualMap_trans {M₃ : Type*} [AddCommGroup M₃] [Module R M
   rfl
 #align linear_equiv.dual_map_trans LinearEquiv.dualMap_trans
 
+@[simp]
+lemma Dual.apply_one_mul_eq (f : Dual R R) (r : R) :
+    f 1 * r = f r := by
+  conv_rhs => rw [← mul_one r, ← smul_eq_mul]
+  rw [map_smul, smul_eq_mul, mul_comm]
+
+@[simp]
+lemma LinearMap.range_dualMap_dual_eq_span_singleton (f : Dual R M₁) :
+    range f.dualMap = R ∙ f := by
+  ext m
+  rw [Submodule.mem_span_singleton]
+  refine ⟨fun ⟨r, hr⟩ ↦ ⟨r 1, ?_⟩, fun ⟨r, hr⟩ ↦ ⟨r • LinearMap.id, ?_⟩⟩
+  · ext; simp [dualMap_apply', ← hr]
+  · ext; simp [dualMap_apply', ← hr]
+
 end DualMap
 
 namespace Basis

This shortens Mathlib.LinearAlgebra.Basic, which is both longer than we like and doesn't have a clear scope.

@@ -3,6 +3,7 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
 -/
+import Mathlib.Algebra.EuclideanDomain.Instances
 import Mathlib.LinearAlgebra.FiniteDimensional
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition

Also use lowercase for DualBases axioms.

@@ -340,7 +340,7 @@ theorem toDual_eq_repr (m : M) (i : ι) : b.toDual m (b i) = b.repr m i :=
   b.toDual_apply_left m i
 #align basis.to_dual_eq_repr Basis.toDual_eq_repr
 
-theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.equivFun m i := by
+theorem toDual_eq_equivFun [Finite ι] (m : M) (i : ι) : b.toDual m (b i) = b.equivFun m i := by
   rw [b.equivFun_apply, toDual_eq_repr]
 #align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFun
 
@@ -461,7 +461,7 @@ theorem toDual_toDual : b.dualBasis.toDual.comp b.toDual = Dual.eval R M := by
 
 end Finite
 
-theorem dualBasis_equivFun [Fintype ι] (l : Dual R M) (i : ι) :
+theorem dualBasis_equivFun [Finite ι] (l : Dual R M) (i : ι) :
     b.dualBasis.equivFun l i = l (b i) := by rw [Basis.equivFun_apply, dualBasis_repr]
 #align basis.dual_basis_equiv_fun Basis.dualBasis_equivFun
 
@@ -743,8 +743,8 @@ elab "use_finite_instance" : tactic => evalUseFiniteInstance
 -- @[nolint has_nonempty_instance] Porting note: removed
 structure Module.DualBases (e : ι → M) (ε : ι → Dual R M) : Prop where
   eval : ∀ i j : ι, ε i (e j) = if i = j then 1 else 0
-  Total : ∀ {m : M}, (∀ i, ε i m = 0) → m = 0
-  Finite : ∀ m : M, { i | ε i m ≠ 0 }.Finite := by
+  protected total : ∀ {m : M}, (∀ i, ε i m = 0) → m = 0
+  protected finite : ∀ m : M, { i | ε i m ≠ 0 }.Finite := by
       use_finite_instance
 #align module.dual_bases Module.DualBases
 
@@ -763,10 +763,8 @@ variable {e : ι → M} {ε : ι → Dual R M}
 /-- The coefficients of `v` on the basis `e` -/
 def coeffs [DecidableEq ι] (h : DualBases e ε) (m : M) : ι →₀ R where
   toFun i := ε i m
-  support := (h.Finite m).toFinset
-  mem_support_toFun := by
-    intro i
-    rw [Set.Finite.mem_toFinset, Set.mem_setOf_eq]
+  support := (h.finite m).toFinset
+  mem_support_toFun i := by rw [Set.Finite.mem_toFinset, Set.mem_setOf_eq]
 #align module.dual_bases.coeffs Module.DualBases.coeffs
 
 @[simp]
@@ -807,12 +805,11 @@ theorem coeffs_lc (l : ι →₀ R) : h.coeffs (DualBases.lc e l) = l := by
 /-- For any m : M n, \sum_{p ∈ Q n} (ε p m) • e p = m -/
 @[simp]
 theorem lc_coeffs (m : M) : DualBases.lc e (h.coeffs m) = m := by
-  refine' eq_of_sub_eq_zero (h.Total _)
-  intro i
+  refine eq_of_sub_eq_zero <| h.total fun i ↦ ?_
   simp [LinearMap.map_sub, h.dual_lc, sub_eq_zero]
 #align module.dual_bases.lc_coeffs Module.DualBases.lc_coeffs
 
-/-- `(h : dual_bases e ε).basis` shows the family of vectors `e` forms a basis. -/
+/-- `(h : DualBases e ε).basis` shows the family of vectors `e` forms a basis. -/
 @[simps]
 def basis : Basis ι R M :=
   Basis.ofRepr
@@ -850,7 +847,7 @@ theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '
   rwa [← lc_def, h.dual_lc] at hi
 #align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_span
 
-theorem coe_dualBasis [Fintype ι] : ⇑h.basis.dualBasis = ε :=
+theorem coe_dualBasis [_root_.Finite ι] : ⇑h.basis.dualBasis = ε :=
   funext fun i =>
     h.basis.ext fun j => by
       rw [h.basis.dualBasis_apply_self, h.coe_basis, h.eval, if_congr eq_comm rfl rfl]

and a few more to clarify that they are about IsEmpty, not about ∅. Make a few more lemmas simp.`

@@ -1547,7 +1547,7 @@ theorem dualAnnihilator_iInf_eq {ι : Type*} [Finite ι] (W : ι → Subspace K
   · intro α β h hyp W
     rw [← h.iInf_comp, hyp _, ← h.iSup_comp]
   · intro W
-    rw [iSup_of_empty', iInf_of_empty', sInf_empty, sSup_empty, dualAnnihilator_top]
+    rw [iSup_of_empty', iInf_of_isEmpty, sInf_empty, sSup_empty, dualAnnihilator_top]
   · intro α _ h W
     rw [iInf_option, iSup_option, dualAnnihilator_inf_eq, h]
 #align subspace.dual_annihilator_infi_eq Subspace.dualAnnihilator_iInf_eq

@@ -1422,7 +1422,9 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M
   have := range_dualMap_eq_dualAnnihilator_ker_of_surjective f.rangeRestrict rr_surj
   convert this using 1
   -- Porting note: broken dot notation lean4#1910
-  · change range ((range f).subtype.comp f.rangeRestrict).dualMap = _
+  · calc
+      _ = range ((range f).subtype.comp f.rangeRestrict).dualMap := by simp
+      _ = _ := ?_
     rw [← dualMap_comp_dualMap, range_comp_of_range_eq_top]
     rwa [range_eq_top]
   · apply congr_arg

This follows up from #9785, which renamed FunLike to DFunLike, by introducing a new abbreviation FunLike F α β := DFunLike F α (fun _ => β), to make the non-dependent use of FunLike easier.

I searched for the pattern DFunLike.*fun and DFunLike.*λ in all files to replace expressions of the form DFunLike F α (fun _ => β) with FunLike F α β. I did this everywhere except for extends clauses for two reasons: it would conflict with #8386, and more importantly extends must directly refer to a structure with no unfolding of defs or abbrevs.

@@ -1295,7 +1295,7 @@ def dualCopairing (W : Submodule R M) : W.dualAnnihilator →ₗ[R] M ⧸ W →
 #align submodule.dual_copairing Submodule.dualCopairing
 
 -- Porting note: helper instance
-instance (W : Submodule R M) : DFunLike (W.dualAnnihilator) M fun _ => R :=
+instance (W : Submodule R M) : FunLike (W.dualAnnihilator) M R :=
   { coe := fun φ => φ.val,
     coe_injective' := fun φ ψ h => by
       ext

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -345,7 +345,7 @@ theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.
 #align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFun
 
 theorem toDual_injective : Injective b.toDual := fun x y h ↦ b.ext_elem_iff.mpr fun i ↦ by
-  simp_rw [← toDual_eq_repr]; exact FunLike.congr_fun h _
+  simp_rw [← toDual_eq_repr]; exact DFunLike.congr_fun h _
 
 theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
   b.toDual_injective (by rwa [_root_.map_zero])
@@ -687,7 +687,7 @@ lemma equiv [IsReflexive R M] (e : M ≃ₗ[R] N) : IsReflexive R N where
     let ed : Dual R (Dual R N) ≃ₗ[R] Dual R (Dual R M) := e.symm.dualMap.dualMap
     have : Dual.eval R N = ed.symm.comp ((Dual.eval R M).comp e.symm.toLinearMap) := by
       ext m f
-      exact FunLike.congr_arg f (e.apply_symm_apply m).symm
+      exact DFunLike.congr_arg f (e.apply_symm_apply m).symm
     simp only [this, LinearEquiv.trans_symm, LinearEquiv.symm_symm, LinearEquiv.dualMap_symm,
       coe_comp, LinearEquiv.coe_coe, EquivLike.comp_bijective]
     exact Bijective.comp (bijective_dual_eval R M) (LinearEquiv.bijective _)
@@ -1106,7 +1106,7 @@ variable {W : Subspace K V}
 
 @[simp]
 theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w :=
-  congr_arg φ <| FunLike.congr_fun
+  congr_arg φ <| DFunLike.congr_fun
     (Classical.choose_spec <| W.subtype.exists_leftInverse_of_injective W.ker_subtype) w
 #align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtype
 
@@ -1295,7 +1295,7 @@ def dualCopairing (W : Submodule R M) : W.dualAnnihilator →ₗ[R] M ⧸ W →
 #align submodule.dual_copairing Submodule.dualCopairing
 
 -- Porting note: helper instance
-instance (W : Submodule R M) : FunLike (W.dualAnnihilator) M fun _ => R :=
+instance (W : Submodule R M) : DFunLike (W.dualAnnihilator) M fun _ => R :=
   { coe := fun φ => φ.val,
     coe_injective' := fun φ ψ h => by
       ext
@@ -1390,7 +1390,7 @@ theorem quotDualCoannihilatorToDual_injective (W : Submodule R (Dual R M)) :
 
 theorem flip_quotDualCoannihilatorToDual_injective (W : Submodule R (Dual R M)) :
     Function.Injective W.quotDualCoannihilatorToDual.flip :=
-  fun _ _ he ↦ Subtype.ext <| LinearMap.ext fun m ↦ FunLike.congr_fun he ⟦m⟧
+  fun _ _ he ↦ Subtype.ext <| LinearMap.ext fun m ↦ DFunLike.congr_fun he ⟦m⟧
 
 open LinearMap in
 theorem quotDualCoannihilatorToDual_nondegenerate (W : Submodule R (Dual R M)) :

Also add some API for related results such as LinearMap.dualCoannihilator_range_eq_ker_flip, which is not needed here but worth having.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -912,6 +912,7 @@ def dualCoannihilator (Φ : Submodule R (Module.Dual R M)) : Submodule R M :=
   Φ.dualAnnihilator.comap (Module.Dual.eval R M)
 #align submodule.dual_coannihilator Submodule.dualCoannihilator
 
+@[simp]
 theorem mem_dualCoannihilator {Φ : Submodule R (Module.Dual R M)} (x : M) :
     x ∈ Φ.dualCoannihilator ↔ ∀ φ ∈ Φ, (φ x : R) = 0 := by
   simp_rw [dualCoannihilator, mem_comap, mem_dualAnnihilator, Module.Dual.eval_apply]
@@ -1428,6 +1429,15 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M
     exact (ker_rangeRestrict f).symm
 #align linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective
 
+theorem ker_dualMap_eq_dualCoannihilator_range (f : M →ₗ[R] M') :
+    LinearMap.ker f.dualMap = (Dual.eval R M' ∘ₗ f).range.dualCoannihilator := by
+  ext x; simp [ext_iff (f := dualMap f x)]
+
+@[simp]
+lemma dualCoannihilator_range_eq_ker_flip (B : M →ₗ[R] M' →ₗ[R] R) :
+    (range B).dualCoannihilator = LinearMap.ker B.flip := by
+  ext x; simp [ext_iff (f := B.flip x)]
+
 end LinearMap
 
 end CommRing
@@ -1595,6 +1605,12 @@ theorem dualMap_bijective_iff {f : V₁ →ₗ[K] V₂} :
 
 variable {B : V₁ →ₗ[K] V₂ →ₗ[K] K}
 
+@[simp]
+lemma dualAnnihilator_ker_eq_range_flip [IsReflexive K V₂] :
+    (ker B).dualAnnihilator = range B.flip := by
+  change _ = range (B.dualMap.comp (Module.evalEquiv K V₂).toLinearMap)
+  rw [← range_dualMap_eq_dualAnnihilator_ker, range_comp_of_range_eq_top _ (LinearEquiv.range _)]
+
 open Function
 
 theorem flip_injective_iff₁ [FiniteDimensional K V₁] : Injective B.flip ↔ Surjective B := by

The dimension of an infinite dimensional dual space is equal to its cardinality. As a consequence (linearEquiv_dual_iff_finiteDimensional), a vector space is isomorphic to its dual iff it's finite dimensional.

The main argument is from https://mathoverflow.net/a/168624. There is a slicker proof in the field case but Vandermonde determinants don't work in a non-commutative ring.

Resolves TODO item posed by Julian Külshammer

• depends on: #8941
• depends on: #8942

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -90,10 +90,6 @@ The dual space of an $R$-module $M$ is the $R$-module of $R$-linear maps $M \to
   * `Subspace.dualQuotDistrib W` is an equivalence
     `Dual K (V₁ ⧸ W) ≃ₗ[K] Dual K V₁ ⧸ W.dualLift.range` from an arbitrary choice of
     splitting of `V₁`.
-
-## TODO
-
-Erdős-Kaplansky theorem about the dimension of a dual vector space in case of infinite dimension.
 -/
 
 noncomputable section
@@ -408,6 +404,18 @@ theorem toDualEquiv_apply (m : M) : b.toDualEquiv m = b.toDual m :=
   rfl
 #align basis.to_dual_equiv_apply Basis.toDualEquiv_apply
 
+-- Not sure whether this is true for free modules over a commutative ring
+/-- A vector space over a field is isomorphic to its dual if and only if it is finite-dimensional:
+  a consequence of the Erdős-Kaplansky theorem. -/
+theorem linearEquiv_dual_iff_finiteDimensional [Field K] [AddCommGroup V] [Module K V] :
+    Nonempty (V ≃ₗ[K] Dual K V) ↔ FiniteDimensional K V := by
+  refine ⟨fun ⟨e⟩ ↦ ?_, fun h ↦ ⟨(Module.Free.chooseBasis K V).toDualEquiv⟩⟩
+  rw [FiniteDimensional, ← Module.rank_lt_alpeh0_iff]
+  by_contra!
+  apply (lift_rank_lt_rank_dual this).ne
+  have := e.lift_rank_eq
+  rwa [lift_umax.{uV,uK}, lift_id'.{uV,uK}] at this
+
 /-- Maps a basis for `V` to a basis for the dual space. -/
 def dualBasis : Basis ι R (Dual R M) :=
   b.map b.toDualEquiv

• Introduce the nondegenerate pairing ((flip_)quotDualCoannihilatorToDual_injective) between M ⧸ W.dualCoannihilator and W . If M is a vector space and W is a finite-dimensional subspace of its dual, this is a perfect pairing (quotDualCoannihilatorToDual_bijective), and W is equal to the annihilator of its coannihilator.

• Use this pairing to show that dualAnnihilator and dualCoannihilator give an antitone order isomorphism orderIsoFiniteCodimDim between finite-codimensional subspaces in a vector space and finite-dimensional subspaces in its dual. This result can be e.g. found in Bourbaki's Algebra. For a finite-dimensional vector space, this gives an OrderIso between all subspaces and all subspaces of the dual.

• Add some lemmas about the image and preimage of annihilators and coannihilators under Dual.eval.

• Expand the docstring of basis_finite_of_finite_spans with comments on generalizations.

• depends on: #8820

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -62,6 +62,9 @@ The dual space of an $R$-module $M$ is the $R$-module of $R$-linear maps $M \to
     `LinearMap.range_dual_map_eq_dualAnnihilator_ker`.
   * `Submodule.dualQuotEquivDualAnnihilator` is the equivalence
     `Dual R (M ⧸ W) ≃ₗ[R] W.dualAnnihilator`
+  * `Submodule.quotDualCoannihilatorToDual` is the nondegenerate pairing
+    `M ⧸ W.dualCoannihilator →ₗ[R] Dual R W`.
+    It is an perfect pairing when `R` is a field and `W` is finite-dimensional.
 * Vector spaces:
   * `Subspace.dualAnnihilator_dualConnihilator_eq` says that the double dual annihilator,
     pulled back ground `Module.Dual.eval`, is the original submodule.
@@ -76,6 +79,10 @@ The dual space of an $R$-module $M$ is the $R$-module of $R$-linear maps $M \to
   * `Module.evalEquiv` is the equivalence `V ≃ₗ[K] Dual K (Dual K V)`
   * `Module.mapEvalEquiv` is the order isomorphism between subspaces of `V` and
     subspaces of `Dual K (Dual K V)`.
+  * `Subspace.orderIsoFiniteCodimDim` is the antitone order isomorphism between
+    finite-codimensional subspaces of `V` and finite-dimensional subspaces of `Dual K V`.
+  * `Subspace.orderIsoFiniteDimensional` is the antitone order isomorphism between
+    subspaces of a finite-dimensional vector space `V` and subspaces of its dual.
   * `Subspace.quotDualEquivAnnihilator W` is the equivalence
     `(Dual K V ⧸ W.dualLift.range) ≃ₗ[K] W.dualAnnihilator`, where `W.dualLift.range` is a copy
     of `Dual K W` inside `Dual K V`.
@@ -902,7 +909,15 @@ theorem mem_dualCoannihilator {Φ : Submodule R (Module.Dual R M)} (x : M) :
   simp_rw [dualCoannihilator, mem_comap, mem_dualAnnihilator, Module.Dual.eval_apply]
 #align submodule.mem_dual_coannihilator Submodule.mem_dualCoannihilator
 
-theorem dualAnnihilator_gc (R M : Type*) [CommSemiring R] [AddCommMonoid M] [Module R M] :
+theorem comap_dualAnnihilator (Φ : Submodule R (Module.Dual R M)) :
+    Φ.dualAnnihilator.comap (Module.Dual.eval R M) = Φ.dualCoannihilator := rfl
+
+theorem map_dualCoannihilator_le (Φ : Submodule R (Module.Dual R M)) :
+    Φ.dualCoannihilator.map (Module.Dual.eval R M) ≤ Φ.dualAnnihilator :=
+  map_le_iff_le_comap.mpr (comap_dualAnnihilator Φ).le
+
+variable (R M) in
+theorem dualAnnihilator_gc :
     GaloisConnection
       (OrderDual.toDual ∘ (dualAnnihilator : Submodule R M → Submodule R (Module.Dual R M)))
       (dualCoannihilator ∘ OrderDual.ofDual) := by
@@ -1042,6 +1057,14 @@ theorem forall_mem_dualAnnihilator_apply_eq_zero_iff (W : Subspace K V) (v : V)
   rw [← SetLike.ext_iff.mp dualAnnihilator_dualCoannihilator_eq v, mem_dualCoannihilator]
 #align subspace.forall_mem_dual_annihilator_apply_eq_zero_iff Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff
 
+theorem comap_dualAnnihilator_dualAnnihilator (W : Subspace K V) :
+    W.dualAnnihilator.dualAnnihilator.comap (Module.Dual.eval K V) = W := by
+  ext; rw [Iff.comm, ← forall_mem_dualAnnihilator_apply_eq_zero_iff]; simp
+
+theorem map_le_dualAnnihilator_dualAnnihilator (W : Subspace K V) :
+    W.map (Module.Dual.eval K V) ≤ W.dualAnnihilator.dualAnnihilator :=
+  map_le_iff_le_comap.mpr (comap_dualAnnihilator_dualAnnihilator W).ge
+
 /-- `Submodule.dualAnnihilator` and `Submodule.dualCoannihilator` form a Galois coinsertion. -/
 def dualAnnihilatorGci (K V : Type*) [Field K] [AddCommGroup V] [Module K V] :
     GaloisCoinsertion
@@ -1145,8 +1168,6 @@ section
 
 open FiniteDimensional
 
-variable {V₁ : Type*} [AddCommGroup V₁] [Module K V₁]
-
 instance instModuleDualFiniteDimensional [FiniteDimensional K V] :
     FiniteDimensional K (Module.Dual K V) := by
   infer_instance
@@ -1154,7 +1175,7 @@ instance instModuleDualFiniteDimensional [FiniteDimensional K V] :
 
 @[simp]
 theorem dual_finrank_eq : finrank K (Module.Dual K V) = finrank K V := by
-  by_cases h : Module.Finite K V
+  by_cases h : FiniteDimensional K V
   · classical exact LinearEquiv.finrank_eq (Basis.ofVectorSpace K V).toDualEquiv.symm
   rw [finrank_eq_zero_of_basis_imp_false, finrank_eq_zero_of_basis_imp_false]
   · exact fun _ b ↦ h (Module.Finite.of_basis b)
@@ -1308,7 +1329,7 @@ theorem range_dualMap_mkQ_eq (W : Submodule R M) :
     exists W.dualCopairing ⟨φ, hφ⟩
 #align submodule.range_dual_map_mkq_eq Submodule.range_dualMap_mkQ_eq
 
-/-- Equivalence $(M/W)^* \approx \operatorname{ann}(W)$. That is, there is a one-to-one
+/-- Equivalence $(M/W)^* \cong \operatorname{ann}(W)$. That is, there is a one-to-one
 correspondence between the dual of `M ⧸ W` and those elements of the dual of `M` that
 vanish on `W`.
 
@@ -1339,6 +1360,37 @@ theorem dualQuotEquivDualAnnihilator_symm_apply_mk (W : Submodule R M) (φ : W.d
   rfl
 #align submodule.dual_quot_equiv_dual_annihilator_symm_apply_mk Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk
 
+theorem finite_dualAnnihilator_iff {W : Submodule R M} [Free R (M ⧸ W)] :
+    Finite R W.dualAnnihilator ↔ Finite R (M ⧸ W) :=
+  (Finite.equiv_iff W.dualQuotEquivDualAnnihilator.symm).trans (finite_dual_iff R)
+
+open LinearMap in
+/-- The pairing between a submodule `W` of a dual module `Dual R M` and the quotient of
+`M` by the coannihilator of `W`, which is always nondegenerate. -/
+def quotDualCoannihilatorToDual (W : Submodule R (Dual R M)) :
+    M ⧸ W.dualCoannihilator →ₗ[R] Dual R W :=
+  liftQ _ (flip <| Submodule.subtype _) le_rfl
+
+@[simp]
+theorem quotDualCoannihilatorToDual_apply (W : Submodule R (Dual R M)) (m : M) (w : W) :
+    W.quotDualCoannihilatorToDual (Quotient.mk m) w = w.1 m := rfl
+
+theorem quotDualCoannihilatorToDual_injective (W : Submodule R (Dual R M)) :
+    Function.Injective W.quotDualCoannihilatorToDual :=
+  LinearMap.ker_eq_bot.mp (ker_liftQ_eq_bot _ _ _ le_rfl)
+
+theorem flip_quotDualCoannihilatorToDual_injective (W : Submodule R (Dual R M)) :
+    Function.Injective W.quotDualCoannihilatorToDual.flip :=
+  fun _ _ he ↦ Subtype.ext <| LinearMap.ext fun m ↦ FunLike.congr_fun he ⟦m⟧
+
+open LinearMap in
+theorem quotDualCoannihilatorToDual_nondegenerate (W : Submodule R (Dual R M)) :
+    W.quotDualCoannihilatorToDual.Nondegenerate := by
+  rw [Nondegenerate, separatingLeft_iff_ker_eq_bot, separatingRight_iff_flip_ker_eq_bot]
+  letI : AddCommGroup W := inferInstance
+  simp_rw [ker_eq_bot]
+  exact ⟨W.quotDualCoannihilatorToDual_injective, W.flip_quotDualCoannihilatorToDual_injective⟩
+
 end Submodule
 
 namespace LinearMap
@@ -1557,6 +1609,77 @@ theorem flip_bijective_iff₂ [FiniteDimensional K V₂] : Bijective B.flip ↔
 
 end LinearMap
 
+namespace Subspace
+
+variable {K V : Type*} [Field K] [AddCommGroup V] [Module K V]
+
+theorem quotDualCoannihilatorToDual_bijective (W : Subspace K (Dual K V)) [FiniteDimensional K W] :
+    Function.Bijective W.quotDualCoannihilatorToDual :=
+  ⟨W.quotDualCoannihilatorToDual_injective, letI : AddCommGroup W := inferInstance
+    flip_injective_iff₂.mp W.flip_quotDualCoannihilatorToDual_injective⟩
+
+theorem flip_quotDualCoannihilatorToDual_bijective (W : Subspace K (Dual K V))
+    [FiniteDimensional K W] : Function.Bijective W.quotDualCoannihilatorToDual.flip :=
+  letI : AddCommGroup W := inferInstance
+  flip_bijective_iff₂.mpr W.quotDualCoannihilatorToDual_bijective
+
+theorem dualCoannihilator_dualAnnihilator_eq {W : Subspace K (Dual K V)} [FiniteDimensional K W] :
+    W.dualCoannihilator.dualAnnihilator = W :=
+  let e := (LinearEquiv.ofBijective _ W.flip_quotDualCoannihilatorToDual_bijective).trans
+    (Submodule.dualQuotEquivDualAnnihilator _)
+  letI : AddCommGroup W := inferInstance
+  haveI : FiniteDimensional K W.dualCoannihilator.dualAnnihilator := LinearEquiv.finiteDimensional e
+  (eq_of_le_of_finrank_eq W.le_dualCoannihilator_dualAnnihilator e.finrank_eq).symm
+
+theorem finiteDimensional_quot_dualCoannihilator_iff {W : Submodule K (Dual K V)} :
+    FiniteDimensional K (V ⧸ W.dualCoannihilator) ↔ FiniteDimensional K W :=
+  ⟨fun _ ↦ FiniteDimensional.of_injective _ W.flip_quotDualCoannihilatorToDual_injective,
+    fun _ ↦ have := Basis.dual_finite (R := K) (M := W)
+    FiniteDimensional.of_injective _ W.quotDualCoannihilatorToDual_injective⟩
+
+open OrderDual in
+/-- For any vector space, `dualAnnihilator` and `dualCoannihilator` gives an antitone order
+  isomorphism between the finite-codimensional subspaces in the vector space and the
+  finite-dimensional subspaces in its dual. -/
+def orderIsoFiniteCodimDim :
+    {W : Subspace K V // FiniteDimensional K (V ⧸ W)} ≃o
+    {W : Subspace K (Dual K V) // FiniteDimensional K W}ᵒᵈ where
+  toFun W := toDual ⟨W.1.dualAnnihilator, Submodule.finite_dualAnnihilator_iff.mpr W.2⟩
+  invFun W := ⟨(ofDual W).1.dualCoannihilator,
+    finiteDimensional_quot_dualCoannihilator_iff.mpr (ofDual W).2⟩
+  left_inv _ := Subtype.ext dualAnnihilator_dualCoannihilator_eq
+  right_inv W := have := (ofDual W).2; Subtype.ext dualCoannihilator_dualAnnihilator_eq
+  map_rel_iff' := dualAnnihilator_le_dualAnnihilator_iff
+
+open OrderDual in
+/-- For any finite-dimensional vector space, `dualAnnihilator` and `dualCoannihilator` give
+  an antitone order isomorphism between the subspaces in the vector space and the subspaces
+  in its dual. -/
+def orderIsoFiniteDimensional [FiniteDimensional K V] :
+    Subspace K V ≃o (Subspace K (Dual K V))ᵒᵈ where
+  toFun W := toDual W.dualAnnihilator
+  invFun W := (ofDual W).dualCoannihilator
+  left_inv _ := dualAnnihilator_dualCoannihilator_eq
+  right_inv _ := dualCoannihilator_dualAnnihilator_eq
+  map_rel_iff' := dualAnnihilator_le_dualAnnihilator_iff
+
+open Submodule in
+theorem dualAnnihilator_dualAnnihilator_eq_map (W : Subspace K V) [FiniteDimensional K W] :
+    W.dualAnnihilator.dualAnnihilator = W.map (Dual.eval K V) := by
+  let e1 := (Free.chooseBasis K W).toDualEquiv ≪≫ₗ W.quotAnnihilatorEquiv.symm
+  haveI := e1.finiteDimensional
+  let e2 := (Free.chooseBasis K _).toDualEquiv ≪≫ₗ W.dualAnnihilator.dualQuotEquivDualAnnihilator
+  haveI := LinearEquiv.finiteDimensional (V₂ := W.dualAnnihilator.dualAnnihilator) e2
+  rw [FiniteDimensional.eq_of_le_of_finrank_eq (map_le_dualAnnihilator_dualAnnihilator W)]
+  rw [← (equivMapOfInjective _ (eval_apply_injective K (V := V)) W).finrank_eq, e1.finrank_eq]
+  exact e2.finrank_eq
+
+theorem map_dualCoannihilator (W : Subspace K (Dual K V)) [FiniteDimensional K V] :
+    W.dualCoannihilator.map (Dual.eval K V) = W.dualAnnihilator := by
+  rw [← dualAnnihilator_dualAnnihilator_eq_map, dualCoannihilator_dualAnnihilator_eq]
+
+end Subspace
+
 end FiniteDimensional
 
 end VectorSpace

From the Hairer challenge

• add flip_in/sur/bijective_iff₁₂: if either of the spaces V and W is finite-dimensional, a linear map V → W* is injective/surjective/bijective iff the flipped map W → V* is surjective/injective/bijective.

• also add consequence for SeparatingDual from the projective space thread (cc @smorel394)

• remove the FiniteDimensional condition from dual_finrank_eq, finrank_range_dualMap_eq_finrank_range, and dualMap_injective/bijective_iff, completing two TODO items by @kmill

• add two lemmas toDual_injective and finite_dual_iff

• golf several proofs in LinearAlgebra/Dual

Co-authored-by: Kyle Miller <kmill31415@gmail.com>

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -4,10 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
 -/
 import Mathlib.LinearAlgebra.FiniteDimensional
+import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
+import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathlib.LinearAlgebra.Projection
 import Mathlib.LinearAlgebra.SesquilinearForm
-import Mathlib.RingTheory.Finiteness
-import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 import Mathlib.RingTheory.TensorProduct
 
 #align_import linear_algebra.dual from "leanprover-community/mathlib"@"b1c017582e9f18d8494e5c18602a8cb4a6f843ac"
@@ -229,17 +229,11 @@ theorem LinearMap.dualMap_injective_of_surjective {f : M₁ →ₗ[R] M₂} (hf
 #align linear_map.dual_map_injective_of_surjective LinearMap.dualMap_injective_of_surjective
 
 /-- The `Linear_equiv` version of `LinearMap.dualMap`. -/
-def LinearEquiv.dualMap (f : M₁ ≃ₗ[R] M₂) : Dual R M₂ ≃ₗ[R] Dual R M₁ :=
-  { f.toLinearMap.dualMap with
-    invFun := f.symm.toLinearMap.dualMap
-    left_inv := by
-      intro φ; ext x
-      simp only [LinearMap.dualMap_apply, LinearEquiv.coe_toLinearMap, LinearMap.toFun_eq_coe,
-        LinearEquiv.apply_symm_apply]
-    right_inv := by
-      intro φ; ext x
-      simp only [LinearMap.dualMap_apply, LinearEquiv.coe_toLinearMap, LinearMap.toFun_eq_coe,
-        LinearEquiv.symm_apply_apply] }
+def LinearEquiv.dualMap (f : M₁ ≃ₗ[R] M₂) : Dual R M₂ ≃ₗ[R] Dual R M₁ where
+  __ := f.toLinearMap.dualMap
+  invFun := f.symm.toLinearMap.dualMap
+  left_inv φ := LinearMap.ext fun x ↦ congr_arg φ (f.right_inv x)
+  right_inv φ := LinearMap.ext fun x ↦ congr_arg φ (f.left_inv x)
 #align linear_equiv.dual_map LinearEquiv.dualMap
 
 @[simp]
@@ -347,12 +341,11 @@ theorem toDual_eq_equivFun [Fintype ι] (m : M) (i : ι) : b.toDual m (b i) = b.
   rw [b.equivFun_apply, toDual_eq_repr]
 #align basis.to_dual_eq_equiv_fun Basis.toDual_eq_equivFun
 
-theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 := by
-  rw [← mem_bot R, ← b.repr.ker, mem_ker, LinearEquiv.coe_coe]
-  apply Finsupp.ext
-  intro b
-  rw [← toDual_eq_repr, a]
-  rfl
+theorem toDual_injective : Injective b.toDual := fun x y h ↦ b.ext_elem_iff.mpr fun i ↦ by
+  simp_rw [← toDual_eq_repr]; exact FunLike.congr_fun h _
+
+theorem toDual_inj (m : M) (a : b.toDual m = 0) : m = 0 :=
+  b.toDual_injective (by rwa [_root_.map_zero])
 #align basis.to_dual_inj Basis.toDual_inj
 
 -- Porting note: broken dot notation lean4#1910 LinearMap.ker
@@ -362,10 +355,8 @@ theorem toDual_ker : LinearMap.ker b.toDual = ⊥ :=
 
 -- Porting note: broken dot notation lean4#1910 LinearMap.range
 theorem toDual_range [Finite ι] : LinearMap.range b.toDual = ⊤ := by
-  cases nonempty_fintype ι
   refine' eq_top_iff'.2 fun f => _
-  rw [LinearMap.mem_range]
-  let lin_comb : ι →₀ R := Finsupp.equivFunOnFinite.symm fun i => f.toFun (b i)
+  let lin_comb : ι →₀ R := Finsupp.equivFunOnFinite.symm fun i => f (b i)
   refine' ⟨Finsupp.total ι M R b lin_comb, b.ext fun i => _⟩
   rw [b.toDual_eq_repr _ i, repr_total b]
   rfl
@@ -499,15 +490,9 @@ theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b :
   rw [← coe_dualBasis, total_dualBasis]
 #align basis.total_coord Basis.total_coord
 
--- Porting note: universes very dodgy in Cardinals...
 theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
     Cardinal.lift.{uK,uV} (Module.rank K V) = Module.rank K (Dual K V) := by
-  classical
-    cases nonempty_fintype ι
-    have := LinearEquiv.lift_rank_eq b.toDualEquiv
-    rw [Cardinal.lift_umax.{uV,uK}] at this
-    rw [this, ← Cardinal.lift_umax]
-    apply Cardinal.lift_id
+  classical rw [← lift_umax.{uV,uK}, b.toDualEquiv.lift_rank_eq, lift_id'.{uV,uK}]
 #align basis.dual_rank_eq Basis.dual_rank_eq
 
 end Basis
@@ -533,17 +518,15 @@ theorem eval_ker : LinearMap.ker (eval K V) = ⊥ := by
 theorem map_eval_injective : (Submodule.map (eval K V)).Injective := by
   apply Submodule.map_injective_of_injective
   rw [← LinearMap.ker_eq_bot]
-  apply eval_ker K V
+  exact eval_ker K V
 #align module.map_eval_injective Module.map_eval_injective
 
--- elaborates faster than `exact`
 theorem comap_eval_surjective : (Submodule.comap (eval K V)).Surjective := by
   apply Submodule.comap_surjective_of_injective
   rw [← LinearMap.ker_eq_bot]
-  apply eval_ker K V
+  exact eval_ker K V
 #align module.comap_eval_surjective Module.comap_eval_surjective
 
--- elaborates faster than `exact`
 end
 
 section
@@ -585,6 +568,17 @@ theorem nontrivial_dual_iff :
 instance instNontrivialDual [Nontrivial V] : Nontrivial (Dual K V) :=
   (nontrivial_dual_iff K).mpr inferInstance
 
+theorem finite_dual_iff : Finite K (Dual K V) ↔ Finite K V := by
+  constructor <;> intro h
+  · obtain ⟨⟨ι, b⟩⟩ := Module.Free.exists_basis (R := K) (M := V)
+    nontriviality K
+    obtain ⟨⟨s, span_s⟩⟩ := h
+    classical
+    haveI := (b.linearIndependent.map' _ b.toDual_ker).finite_of_le_span_finite _ s ?_
+    · exact Finite.of_basis b
+    · rw [span_s]; apply le_top
+  · infer_instance
+
 end
 
 theorem dual_rank_eq [Module.Finite K V] :
@@ -609,9 +603,9 @@ Any finitely-generated free module (and thus any finite-dimensional vector space
 See `Module.IsReflexive.of_finite_of_free`. -/
 class IsReflexive : Prop where
   /-- A reflexive module is one for which the natural map to its double dual is a bijection. -/
-  bijective_dual_eval' : Bijective $ Dual.eval R M
+  bijective_dual_eval' : Bijective (Dual.eval R M)
 
-lemma bijective_dual_eval [IsReflexive R M] : Bijective $ Dual.eval R M :=
+lemma bijective_dual_eval [IsReflexive R M] : Bijective (Dual.eval R M) :=
   IsReflexive.bijective_dual_eval'
 
 instance IsReflexive.of_finite_of_free [Finite R M] [Free R M] : IsReflexive R M where
@@ -622,7 +616,7 @@ variable [IsReflexive R M]
 
 /-- The bijection between a reflexive module and its double dual, bundled as a `LinearEquiv`. -/
 def evalEquiv : M ≃ₗ[R] Dual R (Dual R M) :=
-  LinearEquiv.ofBijective _ $ bijective_dual_eval R M
+  LinearEquiv.ofBijective _ (bijective_dual_eval R M)
 #align module.eval_equiv Module.evalEquiv
 
 @[simp] lemma evalEquiv_toLinearMap : evalEquiv R M = Dual.eval R M := rfl
@@ -630,7 +624,7 @@ def evalEquiv : M ≃ₗ[R] Dual R (Dual R M) :=
 
 @[simp] lemma evalEquiv_apply (m : M) : evalEquiv R M m = Dual.eval R M m := rfl
 
-@[simp] lemma apply_evalEquiv_symm_apply (f : Dual R M) (g : Dual R $ Dual R M) :
+@[simp] lemma apply_evalEquiv_symm_apply (f : Dual R M) (g : Dual R (Dual R M)) :
     f ((evalEquiv R M).symm g) = g f := by
   set m := (evalEquiv R M).symm g
   rw [← (evalEquiv R M).apply_symm_apply g, evalEquiv_apply, Dual.eval_apply]
@@ -1034,28 +1028,12 @@ theorem dualCoannihilator_top (W : Subspace K V) :
 @[simp]
 theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
     W.dualAnnihilator.dualCoannihilator = W := by
-  refine' le_antisymm _ (le_dualAnnihilator_dualCoannihilator _)
-  intro v
+  refine le_antisymm (fun v ↦ Function.mtr ?_) (le_dualAnnihilator_dualCoannihilator _)
   simp only [mem_dualAnnihilator, mem_dualCoannihilator]
-  contrapose!
-  intro hv
-  obtain ⟨W', hW⟩ := Submodule.exists_isCompl W
-  obtain ⟨⟨w, w'⟩, rfl, -⟩ := existsUnique_add_of_isCompl_prod hW v
-  have hw'n : (w' : V) ∉ W := by
-    contrapose! hv
-    exact Submodule.add_mem W w.2 hv
-  have hw'nz : w' ≠ 0 := by
-    rintro rfl
-    exact hw'n (Submodule.zero_mem W)
-  rw [Ne.def, ← Module.forall_dual_apply_eq_zero_iff K w'] at hw'nz
-  push_neg at hw'nz
-  obtain ⟨φ, hφ⟩ := hw'nz
-  exists ((LinearMap.ofIsComplProd hW).comp (LinearMap.inr _ _ _)) φ
-  simp only [coe_comp, coe_inr, Function.comp_apply, ofIsComplProd_apply, map_add,
-    ofIsCompl_left_apply, zero_apply, ofIsCompl_right_apply, zero_add, Ne.def]
-  refine' ⟨_, hφ⟩
-  intro v hv
-  apply LinearMap.ofIsCompl_left_apply hW ⟨v, hv⟩
+  rw [← Quotient.mk_eq_zero W, ← Module.forall_dual_apply_eq_zero_iff K]
+  push_neg
+  refine fun ⟨φ, hφ⟩ ↦ ⟨φ.comp W.mkQ, fun w hw ↦ ?_, hφ⟩
+  rw [comp_apply, mkQ_apply, (Quotient.mk_eq_zero W).mpr hw, φ.map_zero]
 #align subspace.dual_annihilator_dual_coannihilator_eq Subspace.dualAnnihilator_dualCoannihilator_eq
 
 -- exact elaborates slowly
@@ -1081,31 +1059,27 @@ theorem dualAnnihilator_le_dualAnnihilator_iff {W W' : Subspace K V} :
 #align subspace.dual_annihilator_le_dual_annihilator_iff Subspace.dualAnnihilator_le_dualAnnihilator_iff
 
 theorem dualAnnihilator_inj {W W' : Subspace K V} :
-    W.dualAnnihilator = W'.dualAnnihilator ↔ W = W' := by
-  constructor
-  · apply (dualAnnihilatorGci K V).l_injective
-  · rintro rfl
-    rfl
+    W.dualAnnihilator = W'.dualAnnihilator ↔ W = W' :=
+  ⟨fun h ↦ (dualAnnihilatorGci K V).l_injective h, congr_arg _⟩
 #align subspace.dual_annihilator_inj Subspace.dualAnnihilator_inj
 
 /-- Given a subspace `W` of `V` and an element of its dual `φ`, `dualLift W φ` is
 an arbitrary extension of `φ` to an element of the dual of `V`.
 That is, `dualLift W φ` sends `w ∈ W` to `φ x` and `x` in a chosen complement of `W` to `0`. -/
 noncomputable def dualLift (W : Subspace K V) : Module.Dual K W →ₗ[K] Module.Dual K V :=
-  let h := Classical.indefiniteDescription _ W.exists_isCompl
-  (LinearMap.ofIsComplProd h.2).comp (LinearMap.inl _ _ _)
+  (Classical.choose <| W.subtype.exists_leftInverse_of_injective W.ker_subtype).dualMap
 #align subspace.dual_lift Subspace.dualLift
 
 variable {W : Subspace K V}
 
 @[simp]
-theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w := by
-  erw [ofIsCompl_left_apply _ w]
-  rfl
+theorem dualLift_of_subtype {φ : Module.Dual K W} (w : W) : W.dualLift φ (w : V) = φ w :=
+  congr_arg φ <| FunLike.congr_fun
+    (Classical.choose_spec <| W.subtype.exists_leftInverse_of_injective W.ker_subtype) w
 #align subspace.dual_lift_of_subtype Subspace.dualLift_of_subtype
 
 theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLift φ w = φ ⟨w, hw⟩ :=
-  by convert dualLift_of_subtype ⟨w, hw⟩
+  dualLift_of_subtype ⟨w, hw⟩
 #align subspace.dual_lift_of_mem Subspace.dualLift_of_mem
 
 @[simp]
@@ -1173,12 +1147,21 @@ open FiniteDimensional
 
 variable {V₁ : Type*} [AddCommGroup V₁] [Module K V₁]
 
-instance instModuleDualFiniteDimensional [H : FiniteDimensional K V] :
+instance instModuleDualFiniteDimensional [FiniteDimensional K V] :
     FiniteDimensional K (Module.Dual K V) := by
   infer_instance
 #align subspace.module.dual.finite_dimensional Subspace.instModuleDualFiniteDimensional
 
-variable [FiniteDimensional K V] [FiniteDimensional K V₁]
+@[simp]
+theorem dual_finrank_eq : finrank K (Module.Dual K V) = finrank K V := by
+  by_cases h : Module.Finite K V
+  · classical exact LinearEquiv.finrank_eq (Basis.ofVectorSpace K V).toDualEquiv.symm
+  rw [finrank_eq_zero_of_basis_imp_false, finrank_eq_zero_of_basis_imp_false]
+  · exact fun _ b ↦ h (Module.Finite.of_basis b)
+  · exact fun _ b ↦ h ((Module.finite_dual_iff K).mp <| Module.Finite.of_basis b)
+#align subspace.dual_finrank_eq Subspace.dual_finrank_eq
+
+variable [FiniteDimensional K V]
 
 theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
     W.dualAnnihilator.dualAnnihilator = Module.mapEvalEquiv K V W := by
@@ -1187,13 +1170,6 @@ theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
   rwa [← OrderIso.symm_apply_eq]
 #align subspace.dual_annihilator_dual_annihilator_eq Subspace.dualAnnihilator_dualAnnihilator_eq
 
--- TODO(kmill): https://github.com/leanprover-community/mathlib/pull/17521#discussion_r1083241963
-@[simp]
-theorem dual_finrank_eq : finrank K (Module.Dual K V) = finrank K V := by
-  classical
-  exact LinearEquiv.finrank_eq (Basis.ofVectorSpace K V).toDualEquiv.symm
-#align subspace.dual_finrank_eq Subspace.dual_finrank_eq
-
 /-- The quotient by the dual is isomorphic to its dual annihilator.  -/
 -- Porting note: broken dot notation lean4#1910 LinearMap.range
 noncomputable def quotDualEquivAnnihilator (W : Subspace K V) :
@@ -1250,15 +1226,10 @@ variable (f : M₁ →ₗ[R] M₂)
 -- Porting note: broken dot notation lean4#1910 LinearMap.ker
 theorem ker_dualMap_eq_dualAnnihilator_range :
     LinearMap.ker f.dualMap = f.range.dualAnnihilator := by
-  ext φ; constructor <;> intro hφ
-  · rw [mem_ker] at hφ
-    rw [Submodule.mem_dualAnnihilator]
-    rintro y ⟨x, rfl⟩
-    rw [← dualMap_apply, hφ, zero_apply]
-  · ext x
-    rw [dualMap_apply]
-    rw [Submodule.mem_dualAnnihilator] at hφ
-    exact hφ (f x) ⟨x, rfl⟩
+  ext
+  simp_rw [mem_ker, ext_iff, Submodule.mem_dualAnnihilator,
+    ← SetLike.mem_coe, range_coe, Set.forall_range_iff]
+  rfl
 #align linear_map.ker_dual_map_eq_dual_annihilator_range LinearMap.ker_dualMap_eq_dualAnnihilator_range
 
 -- Porting note: broken dot notation lean4#1910 LinearMap.range
@@ -1332,7 +1303,7 @@ theorem range_dualMap_mkQ_eq (W : Submodule R M) :
   constructor
   · rintro ⟨ψ, rfl⟩
     have := LinearMap.mem_range_self W.mkQ.dualMap ψ
-    simpa only [ker_mkQ] using LinearMap.range_dualMap_le_dualAnnihilator_ker W.mkQ this
+    simpa only [ker_mkQ] using W.mkQ.range_dualMap_le_dualAnnihilator_ker this
   · intro hφ
     exists W.dualCopairing ⟨φ, hφ⟩
 #align submodule.range_dual_map_mkq_eq Submodule.range_dualMap_mkQ_eq
@@ -1348,13 +1319,7 @@ def dualQuotEquivDualAnnihilator (W : Submodule R M) :
     (W.mkQ.dualMap.codRestrict W.dualAnnihilator fun φ =>
 -- Porting note: broken dot notation lean4#1910 LinearMap.mem_range_self
       W.range_dualMap_mkQ_eq ▸ LinearMap.mem_range_self W.mkQ.dualMap φ)
-    W.dualCopairing
-    (by
-      ext
-      rfl)
-    (by
-      ext
-      rfl)
+    W.dualCopairing (by ext; rfl) (by ext; rfl)
 #align submodule.dual_quot_equiv_dual_annihilator Submodule.dualQuotEquivDualAnnihilator
 
 @[simp]
@@ -1382,18 +1347,8 @@ open Submodule
 
 -- Porting note: broken dot notation lean4#1910 LinearMap.range
 theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
-    (hf : Function.Surjective f) : LinearMap.range f.dualMap = f.ker.dualAnnihilator := by
-  rw [← f.ker.range_dualMap_mkQ_eq]
-  let f' := LinearMap.quotKerEquivOfSurjective f hf
-  trans LinearMap.range (f.dualMap.comp f'.symm.dualMap.toLinearMap)
-  · rw [LinearMap.range_comp_of_range_eq_top]
-    apply LinearEquiv.range
-  · apply congr_arg
-    ext φ x
-    simp only [LinearMap.coe_comp, LinearEquiv.coe_toLinearMap, LinearMap.dualMap_apply,
-      LinearEquiv.dualMap_apply, mkQ_apply, LinearMap.quotKerEquivOfSurjective,
-      LinearEquiv.trans_symm, LinearEquiv.trans_apply, LinearEquiv.ofTop_symm_apply,
-      LinearMap.quotKerEquivRange_symm_apply_image, mkQ_apply, Function.comp]
+    (hf : Function.Surjective f) : LinearMap.range f.dualMap = f.ker.dualAnnihilator :=
+  ((f.quotKerEquivOfSurjective hf).dualMap.range_comp _).trans f.ker.range_dualMap_mkQ_eq
 #align linear_map.range_dual_map_eq_dual_annihilator_ker_of_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective
 
 -- Note, this can be specialized to the case where `R` is an injective `R`-module, or when
@@ -1402,16 +1357,15 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective (f : M
     (hf : Function.Surjective f.range.subtype.dualMap) :
     LinearMap.range f.dualMap = f.ker.dualAnnihilator := by
   have rr_surj : Function.Surjective f.rangeRestrict := by
-    rw [← LinearMap.range_eq_top, LinearMap.range_rangeRestrict]
+    rw [← range_eq_top, range_rangeRestrict]
   have := range_dualMap_eq_dualAnnihilator_ker_of_surjective f.rangeRestrict rr_surj
   convert this using 1
   -- Porting note: broken dot notation lean4#1910
-  · change LinearMap.range
-      ((Submodule.subtype <| LinearMap.range f).comp f.rangeRestrict).dualMap = _
-    rw [← LinearMap.dualMap_comp_dualMap, LinearMap.range_comp_of_range_eq_top]
-    rwa [LinearMap.range_eq_top]
+  · change range ((range f).subtype.comp f.rangeRestrict).dualMap = _
+    rw [← dualMap_comp_dualMap, range_comp_of_range_eq_top]
+    rwa [range_eq_top]
   · apply congr_arg
-    exact (LinearMap.ker_rangeRestrict f).symm
+    exact (ker_rangeRestrict f).symm
 #align linear_map.range_dual_map_eq_dual_annihilator_ker_of_subtype_range_surjective LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective
 
 end LinearMap
@@ -1433,15 +1387,9 @@ theorem dualPairing_nondegenerate : (dualPairing K V₁).Nondegenerate :=
 #align linear_map.dual_pairing_nondegenerate LinearMap.dualPairing_nondegenerate
 
 theorem dualMap_surjective_of_injective {f : V₁ →ₗ[K] V₂} (hf : Function.Injective f) :
-    Function.Surjective f.dualMap := by
-  intro φ
-  let f' := LinearEquiv.ofInjective f hf
-  use Subspace.dualLift (range f) (f'.symm.dualMap φ)
-  ext x
-  rw [LinearMap.dualMap_apply, Subspace.dualLift_of_mem (mem_range_self f x),
-    LinearEquiv.dualMap_apply]
-  congr 1
-  exact LinearEquiv.symm_apply_apply f' x
+    Function.Surjective f.dualMap := fun φ ↦
+  have ⟨f', hf'⟩ := f.exists_leftInverse_of_injective (ker_eq_bot.mpr hf)
+  ⟨φ.comp f', ext fun x ↦ congr(φ <| $hf' x)⟩
 #align linear_map.dual_map_surjective_of_injective LinearMap.dualMap_surjective_of_injective
 
   -- Porting note: broken dot notation lean4#1910 LinearMap.range
@@ -1455,8 +1403,8 @@ theorem range_dualMap_eq_dualAnnihilator_ker (f : V₁ →ₗ[K] V₂) :
 @[simp]
 theorem dualMap_surjective_iff {f : V₁ →ₗ[K] V₂} :
     Function.Surjective f.dualMap ↔ Function.Injective f := by
-  rw [← LinearMap.range_eq_top, range_dualMap_eq_dualAnnihilator_ker, ←
-    Submodule.dualAnnihilator_bot, Subspace.dualAnnihilator_inj, LinearMap.ker_eq_bot]
+  rw [← LinearMap.range_eq_top, range_dualMap_eq_dualAnnihilator_ker,
+      ← Submodule.dualAnnihilator_bot, Subspace.dualAnnihilator_inj, LinearMap.ker_eq_bot]
 #align linear_map.dual_map_surjective_iff LinearMap.dualMap_surjective_iff
 
 end LinearMap
@@ -1523,7 +1471,7 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
 theorem dualAnnihilator_iInf_eq {ι : Type*} [Finite ι] (W : ι → Subspace K V₁) :
     (⨅ i : ι, W i).dualAnnihilator = ⨆ i : ι, (W i).dualAnnihilator := by
   revert ι
-  refine' @Finite.induction_empty_option _ _ _ _
+  apply Finite.induction_empty_option
   · intro α β h hyp W
     rw [← h.iInf_comp, hyp _, ← h.iSup_comp]
   · intro W
@@ -1555,41 +1503,27 @@ section FiniteDimensional
 
 open FiniteDimensional LinearMap
 
-variable [FiniteDimensional K V₂]
-
 namespace LinearMap
 
--- TODO(kmill) remove finite_dimensional if possible
--- see https://github.com/leanprover-community/mathlib/pull/17521#discussion_r1083242551
 @[simp]
 theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
     -- Porting note: broken dot notation lean4#1910
     finrank K (LinearMap.range f.dualMap) = finrank K (LinearMap.range f) := by
-  have that := Submodule.finrank_quotient_add_finrank (LinearMap.range f)
-  -- Porting note: Again LinearEquiv.finrank_eq needs help
-  let equiv := (Subspace.quotEquivAnnihilator <| LinearMap.range f)
-  have eq := LinearEquiv.finrank_eq (R := K) (M := (V₂ ⧸ range f))
-    (M₂ := { x // x ∈ Submodule.dualAnnihilator (range f) }) equiv
-  rw [eq, ← ker_dualMap_eq_dualAnnihilator_range] at that
-  -- Porting note: cannot convert at `this`?
-  conv_rhs at that => rw [← Subspace.dual_finrank_eq]
-  refine' add_left_injective (finrank K <| LinearMap.ker f.dualMap) _
-  change _ + _ = _ + _
-  rw [finrank_range_add_finrank_ker f.dualMap, add_comm, that]
+  rw [congr_arg dualMap (show f = (range f).subtype.comp f.rangeRestrict by rfl),
+    ← dualMap_comp_dualMap, range_comp,
+    range_eq_top.mpr (dualMap_surjective_of_injective (range f).injective_subtype),
+    Submodule.map_top, finrank_range_of_inj, Subspace.dual_finrank_eq]
+  exact dualMap_injective_of_surjective (range_eq_top.mp f.range_rangeRestrict)
 #align linear_map.finrank_range_dual_map_eq_finrank_range LinearMap.finrank_range_dualMap_eq_finrank_range
 
 /-- `f.dualMap` is injective if and only if `f` is surjective -/
 @[simp]
 theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
     Function.Injective f.dualMap ↔ Function.Surjective f := by
-  refine' ⟨_, fun h => dualMap_injective_of_surjective h⟩
-  rw [← range_eq_top, ← ker_eq_bot]
-  intro h
-  apply Submodule.eq_top_of_finrank_eq
-  rw [← Submodule.finrank_eq_zero] at h
-  rw [← add_zero (FiniteDimensional.finrank K <| LinearMap.range f), ← h, ←
-    LinearMap.finrank_range_dualMap_eq_finrank_range, LinearMap.finrank_range_add_finrank_ker,
-    Subspace.dual_finrank_eq]
+  refine ⟨Function.mtr fun not_surj inj ↦ ?_, dualMap_injective_of_surjective⟩
+  rw [← range_eq_top, ← Ne, ← lt_top_iff_ne_top] at not_surj
+  obtain ⟨φ, φ0, range_le_ker⟩ := (range f).exists_le_ker_of_lt_top not_surj
+  exact φ0 (inj <| ext fun x ↦ range_le_ker ⟨x, rfl⟩)
 #align linear_map.dual_map_injective_iff LinearMap.dualMap_injective_iff
 
 /-- `f.dualMap` is bijective if and only if `f` is -/
@@ -1599,6 +1533,28 @@ theorem dualMap_bijective_iff {f : V₁ →ₗ[K] V₂} :
   simp_rw [Function.Bijective, dualMap_surjective_iff, dualMap_injective_iff, and_comm]
 #align linear_map.dual_map_bijective_iff LinearMap.dualMap_bijective_iff
 
+variable {B : V₁ →ₗ[K] V₂ →ₗ[K] K}
+
+open Function
+
+theorem flip_injective_iff₁ [FiniteDimensional K V₁] : Injective B.flip ↔ Surjective B := by
+  rw [← dualMap_surjective_iff, ← (evalEquiv K V₁).toEquiv.surjective_comp]; rfl
+
+theorem flip_injective_iff₂ [FiniteDimensional K V₂] : Injective B.flip ↔ Surjective B := by
+  rw [← dualMap_injective_iff]; exact (evalEquiv K V₂).toEquiv.injective_comp B.dualMap
+
+theorem flip_surjective_iff₁ [FiniteDimensional K V₁] : Surjective B.flip ↔ Injective B :=
+  flip_injective_iff₂.symm
+
+theorem flip_surjective_iff₂ [FiniteDimensional K V₂] : Surjective B.flip ↔ Injective B :=
+  flip_injective_iff₁.symm
+
+theorem flip_bijective_iff₁ [FiniteDimensional K V₁] : Bijective B.flip ↔ Bijective B := by
+  simp_rw [Bijective, flip_injective_iff₁, flip_surjective_iff₁, and_comm]
+
+theorem flip_bijective_iff₂ [FiniteDimensional K V₂] : Bijective B.flip ↔ Bijective B :=
+  flip_bijective_iff₁.symm
+
 end LinearMap
 
 end FiniteDimensional

A portion of results in Mathlib/LinearAlgebra/FiniteDimensional.lean were generalized to rings and moved to Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean. Most API lemmas for FiniteDimensional are kept but replaced with one lemma proofs. Definitions and niche lemmas are replaced by the generalized version completely.

Co-authored-by: erd1 <the.erd.one@gmail.com> Co-authored-by: Andrew Yang <the.erd.one@gmail.com>

@@ -1586,7 +1586,7 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
   rw [← range_eq_top, ← ker_eq_bot]
   intro h
   apply Submodule.eq_top_of_finrank_eq
-  rw [← finrank_eq_zero] at h
+  rw [← Submodule.finrank_eq_zero] at h
   rw [← add_zero (FiniteDimensional.finrank K <| LinearMap.range f), ← h, ←
     LinearMap.finrank_range_dualMap_eq_finrank_range, LinearMap.finrank_range_add_finrank_ker,
     Subspace.dual_finrank_eq]

@@ -60,7 +60,7 @@ The dual space of an $R$-module $M$ is the $R$-module of $R$-linear maps $M \to
   * `LinearMap.range_dual_map_eq_dualAnnihilator_ker_of_subtype_range_surjective` says that
     `f.dual_map.range = f.ker.dualAnnihilator`; this is specialized to vector spaces in
     `LinearMap.range_dual_map_eq_dualAnnihilator_ker`.
-  * `Submodule.dual_quot_equiv_dualAnnihilator` is the equivalence
+  * `Submodule.dualQuotEquivDualAnnihilator` is the equivalence
     `Dual R (M ⧸ W) ≃ₗ[R] W.dualAnnihilator`
 * Vector spaces:
   * `Subspace.dualAnnihilator_dualConnihilator_eq` says that the double dual annihilator,
@@ -1031,6 +1031,7 @@ theorem dualCoannihilator_top (W : Subspace K V) :
   rw [dualCoannihilator, dualAnnihilator_top, comap_bot, Module.eval_ker]
 #align subspace.dual_coannihilator_top Subspace.dualCoannihilator_top
 
+@[simp]
 theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
     W.dualAnnihilator.dualCoannihilator = W := by
   refine' le_antisymm _ (le_dualAnnihilator_dualCoannihilator _)

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -1569,7 +1569,7 @@ theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
   let equiv := (Subspace.quotEquivAnnihilator <| LinearMap.range f)
   have eq := LinearEquiv.finrank_eq (R := K) (M := (V₂ ⧸ range f))
     (M₂ := { x // x ∈ Submodule.dualAnnihilator (range f) }) equiv
-  rw [eq, ←ker_dualMap_eq_dualAnnihilator_range] at that
+  rw [eq, ← ker_dualMap_eq_dualAnnihilator_range] at that
   -- Porting note: cannot convert at `this`?
   conv_rhs at that => rw [← Subspace.dual_finrank_eq]
   refine' add_left_injective (finrank K <| LinearMap.ker f.dualMap) _

@@ -585,16 +585,6 @@ theorem nontrivial_dual_iff :
 instance instNontrivialDual [Nontrivial V] : Nontrivial (Dual K V) :=
   (nontrivial_dual_iff K).mpr inferInstance
 
-theorem exists_dual_map_eq_bot_of_lt_top {p : Submodule K V} (hp : p < ⊤) (hp' : Free K (V ⧸ p)) :
-    ∃ f : Dual K V, f ≠ 0 ∧ p.map f = ⊥ := by
-  obtain ⟨f, g, h⟩ : Nontrivial (Dual K <| V ⧸ p) :=
-    (nontrivial_dual_iff K).mpr <| Submodule.Quotient.nontrivial_of_lt_top p hp
-  refine ⟨(f - g).comp p.mkQ, ?_, by simp [Submodule.map_comp]⟩
-  replace h : f - g ≠ 0 := sub_ne_zero.mpr h
-  contrapose! h
-  refine Submodule.quot_hom_ext (f := f - g) (g := 0) fun v ↦ (?_ : (f - g).comp p.mkQ v = _)
-  simp [h]
-
 end
 
 theorem dual_rank_eq [Module.Finite K V] :
@@ -703,6 +693,27 @@ end IsReflexive
 
 end Module
 
+namespace Submodule
+
+open Module
+
+variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M] {p : Submodule R M}
+
+theorem exists_dual_map_eq_bot_of_nmem {x : M} (hx : x ∉ p) (hp' : Free R (M ⧸ p)) :
+    ∃ f : Dual R M, f x ≠ 0 ∧ p.map f = ⊥ := by
+  suffices ∃ f : Dual R (M ⧸ p), f (p.mkQ x) ≠ 0 by
+    obtain ⟨f, hf⟩ := this; exact ⟨f.comp p.mkQ, hf, by simp [Submodule.map_comp]⟩
+  rwa [← Submodule.Quotient.mk_eq_zero, ← Submodule.mkQ_apply,
+    ← forall_dual_apply_eq_zero_iff (K := R), not_forall] at hx
+
+theorem exists_dual_map_eq_bot_of_lt_top (hp : p < ⊤) (hp' : Free R (M ⧸ p)) :
+    ∃ f : Dual R M, f ≠ 0 ∧ p.map f = ⊥ := by
+  obtain ⟨x, hx⟩ : ∃ x : M, x ∉ p := by rw [lt_top_iff_ne_top] at hp; contrapose! hp; ext; simp [hp]
+  obtain ⟨f, hf, hf'⟩ := p.exists_dual_map_eq_bot_of_nmem hx hp'
+  exact ⟨f, by aesop, hf'⟩
+
+end Submodule
+
 section DualBases
 
 open Module

In combination with existing work the changes here mean that the following now works (and furthermore, makes no assumptions about characteristic):

example {K L : Type*} [Field K] [IsAlgClosed K] [LieRing L] [LieAlgebra K L]
    [FiniteDimensional K L] [LieAlgebra.IsKilling K L]
    (H : LieSubalgebra K L) [H.IsCartanSubalgebra] :
    Submodule.span K (range (LieModule.weight.toLinear K H L)) = ⊤ := by
  simp

@@ -563,6 +563,38 @@ theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v
   rfl
 #align module.forall_dual_apply_eq_zero_iff Module.forall_dual_apply_eq_zero_iff
 
+@[simp]
+theorem subsingleton_dual_iff :
+    Subsingleton (Dual K V) ↔ Subsingleton V := by
+  refine ⟨fun h ↦ ⟨fun v w ↦ ?_⟩, fun h ↦ ⟨fun f g ↦ ?_⟩⟩
+  · rw [← sub_eq_zero, ← forall_dual_apply_eq_zero_iff K (v - w)]
+    intros f
+    simp [Subsingleton.elim f 0]
+  · ext v
+    simp [Subsingleton.elim v 0]
+
+instance instSubsingletonDual [Subsingleton V] : Subsingleton (Dual K V) :=
+  (subsingleton_dual_iff K).mp inferInstance
+
+@[simp]
+theorem nontrivial_dual_iff :
+    Nontrivial (Dual K V) ↔ Nontrivial V := by
+  rw [← not_iff_not, not_nontrivial_iff_subsingleton, not_nontrivial_iff_subsingleton,
+    subsingleton_dual_iff]
+
+instance instNontrivialDual [Nontrivial V] : Nontrivial (Dual K V) :=
+  (nontrivial_dual_iff K).mpr inferInstance
+
+theorem exists_dual_map_eq_bot_of_lt_top {p : Submodule K V} (hp : p < ⊤) (hp' : Free K (V ⧸ p)) :
+    ∃ f : Dual K V, f ≠ 0 ∧ p.map f = ⊥ := by
+  obtain ⟨f, g, h⟩ : Nontrivial (Dual K <| V ⧸ p) :=
+    (nontrivial_dual_iff K).mpr <| Submodule.Quotient.nontrivial_of_lt_top p hp
+  refine ⟨(f - g).comp p.mkQ, ?_, by simp [Submodule.map_comp]⟩
+  replace h : f - g ≠ 0 := sub_ne_zero.mpr h
+  contrapose! h
+  refine Submodule.quot_hom_ext (f := f - g) (g := 0) fun v ↦ (?_ : (f - g).comp p.mkQ v = _)
+  simp [h]
+
 end
 
 theorem dual_rank_eq [Module.Finite K V] :

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -659,7 +659,7 @@ lemma equiv [IsReflexive R M] (e : M ≃ₗ[R] N) : IsReflexive R N where
       exact FunLike.congr_arg f (e.apply_symm_apply m).symm
     simp only [this, LinearEquiv.trans_symm, LinearEquiv.symm_symm, LinearEquiv.dualMap_symm,
       coe_comp, LinearEquiv.coe_coe, EquivLike.comp_bijective]
-    refine Bijective.comp (bijective_dual_eval R M) (LinearEquiv.bijective _)
+    exact Bijective.comp (bijective_dual_eval R M) (LinearEquiv.bijective _)
 
 instance _root_.MulOpposite.instModuleIsReflexive : IsReflexive R (MulOpposite M) :=
   equiv <| MulOpposite.opLinearEquiv _

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -793,7 +793,7 @@ theorem coe_basis : ⇑h.basis = e := by
 theorem mem_of_mem_span {H : Set ι} {x : M} (hmem : x ∈ Submodule.span R (e '' H)) :
     ∀ i : ι, ε i x ≠ 0 → i ∈ H := by
   intro i hi
-  rcases(Finsupp.mem_span_image_iff_total _).mp hmem with ⟨l, supp_l, rfl⟩
+  rcases (Finsupp.mem_span_image_iff_total _).mp hmem with ⟨l, supp_l, rfl⟩
   apply not_imp_comm.mp ((Finsupp.mem_supported' _ _).mp supp_l i)
   rwa [← lc_def, h.dual_lc] at hi
 #align module.dual_bases.mem_of_mem_span Module.DualBases.mem_of_mem_span

Purely cosmetic PR.

@@ -683,7 +683,7 @@ variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
 open Lean.Elab.Tactic in
 /-- Try using `Set.to_finite` to dispatch a `Set.finite` goal. -/
 def evalUseFiniteInstance : TacticM Unit := do
-  evalTactic (← `(tactic| intros; apply Set.toFinite ))
+  evalTactic (← `(tactic| intros; apply Set.toFinite))
 
 elab "use_finite_instance" : tactic => evalUseFiniteInstance
 

In several places, we unfold Finsupp.sum just to use Finset.sum_eq_single; this adds the missing lemma.

@@ -737,15 +737,13 @@ open Module
 variable [DecidableEq ι] (h : DualBases e ε)
 
 theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i := by
-  erw [_root_.map_sum]
+  rw [lc, _root_.map_finsupp_sum, Finsupp.sum_eq_single i (g := fun a b ↦ (ε i) (b • e a))]
   -- Porting note: cannot get at •
   -- simp only [h.eval, map_smul, smul_eq_mul]
-  rw [Finset.sum_eq_single i]
   · simp [h.eval, smul_eq_mul]
   · intro q _ q_ne
     simp [q_ne.symm, h.eval, smul_eq_mul]
-  · intro p_not_in
-    simp [Finsupp.not_mem_support_iff.1 p_not_in]
+  · simp
 #align module.dual_bases.dual_lc Module.DualBases.dual_lc
 
 @[simp]

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -1521,7 +1521,7 @@ namespace LinearMap
 -- see https://github.com/leanprover-community/mathlib/pull/17521#discussion_r1083242551
 @[simp]
 theorem finrank_range_dualMap_eq_finrank_range (f : V₁ →ₗ[K] V₂) :
-  -- Porting note: broken dot notation lean4#1910
+    -- Porting note: broken dot notation lean4#1910
     finrank K (LinearMap.range f.dualMap) = finrank K (LinearMap.range f) := by
   have that := Submodule.finrank_quotient_add_finrank (LinearMap.range f)
   -- Porting note: Again LinearEquiv.finrank_eq needs help

Also _root_.map_smul when in the neighbourhood.

@@ -299,7 +299,7 @@ theorem toDual_apply (i j : ι) : b.toDual (b i) (b j) = if i = j then 1 else 0
 @[simp]
 theorem toDual_total_left (f : ι →₀ R) (i : ι) :
     b.toDual (Finsupp.total ι M R b f) (b i) = f i := by
-  rw [Finsupp.total_apply, Finsupp.sum, LinearMap.map_sum, LinearMap.sum_apply]
+  rw [Finsupp.total_apply, Finsupp.sum, _root_.map_sum, LinearMap.sum_apply]
   simp_rw [LinearMap.map_smul, LinearMap.smul_apply, toDual_apply, smul_eq_mul, mul_boole,
     Finset.sum_ite_eq']
   split_ifs with h
@@ -310,7 +310,7 @@ theorem toDual_total_left (f : ι →₀ R) (i : ι) :
 @[simp]
 theorem toDual_total_right (f : ι →₀ R) (i : ι) :
     b.toDual (b i) (Finsupp.total ι M R b f) = f i := by
-  rw [Finsupp.total_apply, Finsupp.sum, LinearMap.map_sum]
+  rw [Finsupp.total_apply, Finsupp.sum, _root_.map_sum]
   simp_rw [LinearMap.map_smul, toDual_apply, smul_eq_mul, mul_boole, Finset.sum_ite_eq]
   split_ifs with h
   · rfl
@@ -384,7 +384,7 @@ theorem sum_dual_apply_smul_coord (f : Module.Dual R M) :
     (∑ x, f (b x) • b.coord x) = f := by
   ext m
   simp_rw [LinearMap.sum_apply, LinearMap.smul_apply, smul_eq_mul, mul_comm (f _), ← smul_eq_mul, ←
-    f.map_smul, ← f.map_sum, Basis.coord_apply, Basis.sum_repr]
+    f.map_smul, ← _root_.map_sum, Basis.coord_apply, Basis.sum_repr]
 #align basis.sum_dual_apply_smul_coord Basis.sum_dual_apply_smul_coord
 
 end
@@ -737,7 +737,7 @@ open Module
 variable [DecidableEq ι] (h : DualBases e ε)
 
 theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i := by
-  erw [LinearMap.map_sum]
+  erw [_root_.map_sum]
   -- Porting note: cannot get at •
   -- simp only [h.eval, map_smul, smul_eq_mul]
   rw [Finset.sum_eq_single i]
@@ -1656,7 +1656,7 @@ theorem dualDistrib_dualDistribInvOfBasis_left_inverse (b : Basis ι R M) (c : B
   rintro ⟨i', j'⟩
   simp only [dualDistrib, Basis.coe_dualBasis, coe_comp, Function.comp_apply,
     dualDistribInvOfBasis_apply, Basis.coord_apply, Basis.tensorProduct_repr_tmul_apply,
-    Basis.repr_self, ne_eq, LinearMap.map_sum, map_smul, homTensorHomMap_apply, compRight_apply,
+    Basis.repr_self, ne_eq, _root_.map_sum, map_smul, homTensorHomMap_apply, compRight_apply,
     Basis.tensorProduct_apply, coeFn_sum, Finset.sum_apply, smul_apply, LinearEquiv.coe_coe,
     map_tmul, lid_tmul, smul_eq_mul, id_coe, id_eq]
   rw [Finset.sum_eq_single i, Finset.sum_eq_single j]; simp

We do not want AlgHom to cast to LinearMap via the rarely-used DistribMulActionHom.

The only places this was used are:

• ones that I wrote accidentally, which are replaced with AlgHom.toLinearMap (for which lemmas already exist)
• a non-unital case, where I've inserted the transitive coercion manually (and a TODO); a syntactic change that does not change the underlying term

We could consider adding a LinearMapClass.toLinearMap coercion in a future PR, but I would guess this is just unification hell compared to AlgHom.toLinearMap, so I don't want to volunteer to do it.

@@ -1614,7 +1614,7 @@ variable [Module R M] [Module A M] [Module R N] [IsScalarTower R A M]
 
 /-- Heterobasic version of `TensorProduct.dualDistrib` -/
 def dualDistrib : Dual A M ⊗[R] Dual R N →ₗ[A] Dual A (M ⊗[R] N) :=
-  compRight (Algebra.TensorProduct.rid R A A) ∘ₗ homTensorHomMap R A A M N A R
+  compRight (Algebra.TensorProduct.rid R A A).toLinearMap ∘ₗ homTensorHomMap R A A M N A R
 
 variable {R M N}
 

We clean up heart beat bumps after #6474.

@@ -1426,15 +1426,12 @@ open Submodule
 -- Porting note: remove this at some point; this spends a lot of time
 -- checking that AddCommGroup structures on V₁ ⧸ W.dualAnnihilator are defEq
 -- was much worse with implicit universe variables
-set_option maxHeartbeats 400000 in
 theorem dualPairing_eq (W : Subspace K V₁) :
     W.dualPairing = W.quotAnnihilatorEquiv.toLinearMap := by
   ext
   rfl
 #align subspace.dual_pairing_eq Subspace.dualPairing_eq
 
--- Porting note: remove this
-set_option maxHeartbeats 400000 in
 theorem dualPairing_nondegenerate (W : Subspace K V₁) : W.dualPairing.Nondegenerate := by
   constructor
   · rw [LinearMap.separatingLeft_iff_ker_eq_bot, dualPairing_eq]

In Mathlib/LinearAlgebra/Dual.lean we also overhaul the universe argument names, as the file switched between two conventions and making up undeclared universe variables.

Mathlib/LinearAlgebra/Prod.lean invented some new variables even though it already had plenty available.

@@ -89,17 +89,14 @@ The dual space of an $R$-module $M$ is the $R$-module of $R$-linear maps $M \to
 Erdős-Kaplansky theorem about the dimension of a dual vector space in case of infinite dimension.
 -/
 
-set_option autoImplicit true
-
-
 noncomputable section
 
 namespace Module
 
 -- Porting note: max u v universe issues so name and specific below
-universe u uA v v' v'' w u₁ u₂
+universe uR uA uM uM' uM''
 
-variable (R : Type u) (A : Type uA) (M : Type v)
+variable (R : Type uR) (A : Type uA) (M : Type uM)
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M]
 
@@ -135,7 +132,7 @@ theorem eval_apply (v : M) (a : Dual R M) : eval R M v a = a v :=
   rfl
 #align module.dual.eval_apply Module.Dual.eval_apply
 
-variable {R M} {M' : Type v'}
+variable {R M} {M' : Type uM'}
 variable [AddCommMonoid M'] [Module R M']
 
 /-- The transposition of linear maps, as a linear map from `M →ₗ[R] M'` to
@@ -149,7 +146,7 @@ theorem transpose_apply (u : M →ₗ[R] M') (l : Dual R M') : transpose (R := R
   rfl
 #align module.dual.transpose_apply Module.Dual.transpose_apply
 
-variable {M'' : Type v''} [AddCommMonoid M''] [Module R M'']
+variable {M'' : Type uM''} [AddCommMonoid M''] [Module R M'']
 
 -- Porting note: with reducible def need to specify some parameters to transpose explicitly
 theorem transpose_comp (u : M' →ₗ[R] M'') (v : M →ₗ[R] M') :
@@ -161,7 +158,7 @@ end Dual
 
 section Prod
 
-variable (M' : Type v') [AddCommMonoid M'] [Module R M']
+variable (M' : Type uM') [AddCommMonoid M'] [Module R M']
 
 /-- Taking duals distributes over products. -/
 @[simps!]
@@ -183,6 +180,8 @@ section DualMap
 
 open Module
 
+universe u v v'
+
 variable {R : Type u} [CommSemiring R] {M₁ : Type v} {M₂ : Type v'}
 
 variable [AddCommMonoid M₁] [Module R M₁] [AddCommMonoid M₂] [Module R M₂]
@@ -277,7 +276,8 @@ open Module Module.Dual Submodule LinearMap Cardinal Function
 
 open BigOperators
 
-variable {R : Type u} {M : Type v} {K : Type u₁} {V : Type u₂} {ι : Type w}
+universe uR uM uK uV uι
+variable {R : Type uR} {M : Type uM} {K : Type uK} {V : Type uV} {ι : Type uι}
 
 section CommSemiring
 
@@ -501,11 +501,11 @@ theorem total_coord [CommRing R] [AddCommGroup M] [Module R M] [Finite ι] (b :
 
 -- Porting note: universes very dodgy in Cardinals...
 theorem dual_rank_eq [CommRing K] [AddCommGroup V] [Module K V] [Finite ι] (b : Basis ι K V) :
-    Cardinal.lift.{u₁,u₂} (Module.rank K V) = Module.rank K (Dual K V) := by
+    Cardinal.lift.{uK,uV} (Module.rank K V) = Module.rank K (Dual K V) := by
   classical
     cases nonempty_fintype ι
     have := LinearEquiv.lift_rank_eq b.toDualEquiv
-    rw [Cardinal.lift_umax.{u₂,u₁}] at this
+    rw [Cardinal.lift_umax.{uV,uK}] at this
     rw [this, ← Cardinal.lift_umax]
     apply Cardinal.lift_id
 #align basis.dual_rank_eq Basis.dual_rank_eq
@@ -514,7 +514,8 @@ end Basis
 
 namespace Module
 
-variable {K : Type u₁} {V : Type u₂}
+universe uK uV
+variable {K : Type uK} {V : Type uV}
 
 variable [CommRing K] [AddCommGroup V] [Module K V] [Module.Free K V]
 
@@ -565,7 +566,7 @@ theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v
 end
 
 theorem dual_rank_eq [Module.Finite K V] :
-    Cardinal.lift.{u₁,u₂} (Module.rank K V) = Module.rank K (Dual K V) :=
+    Cardinal.lift.{uK,uV} (Module.rank K V) = Module.rank K (Dual K V) :=
   (Module.Free.chooseBasis K V).dual_rank_eq
 #align module.dual_rank_eq Module.dual_rank_eq
 
@@ -1197,7 +1198,8 @@ open Module
 
 namespace LinearMap
 
-variable {R : Type u} [CommSemiring R] {M₁ : Type v} {M₂ : Type v'}
+universe uR uM₁ uM₂
+variable {R : Type uR} [CommSemiring R] {M₁ : Type uM₁} {M₂ : Type uM₂}
 
 variable [AddCommMonoid M₁] [Module R M₁] [AddCommMonoid M₂] [Module R M₂]
 
@@ -1376,8 +1378,9 @@ end CommRing
 
 section VectorSpace
 
--- Porting note: adding `u` to avoid timeouts in `dualPairing_eq`
-variable {K : Type u} [Field K] {V₁ : Type v'} {V₂ : Type v''}
+-- Porting note: adding `uK` to avoid timeouts in `dualPairing_eq`
+universe uK uV₁ uV₂
+variable {K : Type uK} [Field K] {V₁ : Type uV₁} {V₂ : Type uV₂}
 
 variable [AddCommGroup V₁] [Module K V₁] [AddCommGroup V₂] [Module K V₂]
 

The TODO for this assumed that LinearEquiv.ulift was missing, but in fact it already existed.

@@ -578,7 +578,7 @@ section IsReflexive
 
 open Function
 
-variable (R M : Type*) [CommRing R] [AddCommGroup M] [Module R M]
+variable (R M N : Type*) [CommRing R] [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
 /-- A reflexive module is one for which the natural map to its double dual is a bijection.
 
@@ -637,8 +637,7 @@ theorem mapEvalEquiv_symm_apply (W'' : Submodule R (Dual R (Dual R M))) :
   rfl
 #align module.map_eval_equiv_symm_apply Module.mapEvalEquiv_symm_apply
 
-instance _root_.Prod.instModuleIsReflexive
-    {N : Type*} [AddCommGroup N] [Module R N] [IsReflexive R N] :
+instance _root_.Prod.instModuleIsReflexive [IsReflexive R N] :
     IsReflexive R (M × N) where
   bijective_dual_eval' := by
     let e : Dual R (Dual R (M × N)) ≃ₗ[R] Dual R (Dual R M) × Dual R (Dual R N) :=
@@ -650,19 +649,22 @@ instance _root_.Prod.instModuleIsReflexive
       coe_comp, LinearEquiv.coe_coe, EquivLike.comp_bijective]
     exact Bijective.Prod_map (bijective_dual_eval R M) (bijective_dual_eval R N)
 
-instance _root_.MulOpposite.instModuleIsReflexive : IsReflexive R (MulOpposite M) where
+variable {R M N} in
+lemma equiv [IsReflexive R M] (e : M ≃ₗ[R] N) : IsReflexive R N where
   bijective_dual_eval' := by
-    let e : Dual R (Dual R (MulOpposite M)) ≃ₗ[R] Dual R (Dual R M) :=
-      LinearEquiv.dualMap <| LinearEquiv.dualMap <| MulOpposite.opLinearEquiv _ |>.symm
-    have : Dual.eval R (MulOpposite M) = e.symm.comp ((Dual.eval R M).comp
-        <| MulOpposite.opLinearEquiv _ |>.symm.toLinearMap) := by
-      ext m f; rfl
+    let ed : Dual R (Dual R N) ≃ₗ[R] Dual R (Dual R M) := e.symm.dualMap.dualMap
+    have : Dual.eval R N = ed.symm.comp ((Dual.eval R M).comp e.symm.toLinearMap) := by
+      ext m f
+      exact FunLike.congr_arg f (e.apply_symm_apply m).symm
     simp only [this, LinearEquiv.trans_symm, LinearEquiv.symm_symm, LinearEquiv.dualMap_symm,
       coe_comp, LinearEquiv.coe_coe, EquivLike.comp_bijective]
     refine Bijective.comp (bijective_dual_eval R M) (LinearEquiv.bijective _)
 
--- TODO: add `ULift.instModuleIsReflexive : IsReflexive R (ULift.{v} M)` once we have
--- `LinearEquiv.ulift`
+instance _root_.MulOpposite.instModuleIsReflexive : IsReflexive R (MulOpposite M) :=
+  equiv <| MulOpposite.opLinearEquiv _
+
+instance _root_.ULift.instModuleIsReflexive.{w} : IsReflexive R (ULift.{w} M) :=
+  equiv ULift.moduleEquiv.symm
 
 end IsReflexive
 

It seems that Lean can find LinearMap.instFunLike just fine now. Furthermore, Module.Dual.instFunLikeDual was causing TC synthesis to fail. We delete it.

@@ -124,9 +124,6 @@ namespace Dual
 
 instance : Inhabited (Dual R M) := ⟨0⟩
 
-instance : FunLike (Dual R M) M fun _ => R :=
-  inferInstanceAs (FunLike (M →ₗ[R] R) M fun _ => R)
-
 /-- Maps a module M to the dual of the dual of M. See `Module.erange_coe` and
 `Module.evalEquiv`. -/
 def eval : M →ₗ[R] Dual R (Dual R M) :=

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -738,7 +738,6 @@ variable [DecidableEq ι] (h : DualBases e ε)
 
 theorem dual_lc (l : ι →₀ R) (i : ι) : ε i (DualBases.lc e l) = l i := by
   erw [LinearMap.map_sum]
-  simp_rw [map_smul]
   -- Porting note: cannot get at •
   -- simp only [h.eval, map_smul, smul_eq_mul]
   rw [Finset.sum_eq_single i]

This generalizes the existing BilinForm.tensorDistrib to be heterogenous in the rings it uses, such that a base change,

protected def baseChange (B : BilinForm R M₂) :
  BilinForm A (A ⊗[R] M₂) :=

falls out as a special case. I do not attempt to generalize BilinForm.tensorDistribEquiv.

Unfortunately, this changes the defeq as

-(B₁.tmul B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂'
+(B₁.tmul B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₂ m₂ m₂' • B₁ m₁ m₁'

We could fix this by using the right action instead, but that's a lot of work for a very minorly annoying defeq.

This also breaks the defeq of tensorDistribEquiv B = tensorDistrib B; though the reason is more complicated than the scalar action issue above. It would be fixed if we defined all the homogenous operations on tensor products as special cases of the heterogenous ones, but that's also a lot of work for a very small win.

This is a port of work from https://github.com/pygae/lean-ga/pull/31, and almost at the end of the path to a base change of quadratic forms and clifford algebras.

This was independently developed at the Leiden workshop as BilinForm.baseChange, though the results there are not sorry-free.

@@ -8,6 +8,7 @@ import Mathlib.LinearAlgebra.Projection
 import Mathlib.LinearAlgebra.SesquilinearForm
 import Mathlib.RingTheory.Finiteness
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
+import Mathlib.RingTheory.TensorProduct
 
 #align_import linear_algebra.dual from "leanprover-community/mathlib"@"b1c017582e9f18d8494e5c18602a8cb4a6f843ac"
 
@@ -96,9 +97,9 @@ noncomputable section
 namespace Module
 
 -- Porting note: max u v universe issues so name and specific below
-universe u v v' v'' w u₁ u₂
+universe u uA v v' v'' w u₁ u₂
 
-variable (R : Type u) (M : Type v)
+variable (R : Type u) (A : Type uA) (M : Type v)
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M]
 
@@ -1566,7 +1567,7 @@ end VectorSpace
 
 namespace TensorProduct
 
-variable (R : Type*) (M : Type*) (N : Type*)
+variable (R A : Type*) (M : Type*) (N : Type*)
 
 variable {ι κ : Type*}
 
@@ -1608,6 +1609,24 @@ theorem dualDistrib_apply (f : Dual R M) (g : Dual R N) (m : M) (n : N) :
 
 end
 
+namespace AlgebraTensorModule
+variable [CommSemiring R] [CommSemiring A] [Algebra R A] [AddCommMonoid M] [AddCommMonoid N]
+
+variable [Module R M] [Module A M] [Module R N] [IsScalarTower R A M]
+
+/-- Heterobasic version of `TensorProduct.dualDistrib` -/
+def dualDistrib : Dual A M ⊗[R] Dual R N →ₗ[A] Dual A (M ⊗[R] N) :=
+  compRight (Algebra.TensorProduct.rid R A A) ∘ₗ homTensorHomMap R A A M N A R
+
+variable {R M N}
+
+@[simp]
+theorem dualDistrib_apply (f : Dual A M) (g : Dual R N) (m : M) (n : N) :
+    dualDistrib R A M N (f ⊗ₜ g) (m ⊗ₜ n) = g n • f m :=
+  rfl
+
+end AlgebraTensorModule
+
 variable {R M N}
 
 variable [CommRing R] [AddCommGroup M] [AddCommGroup N]

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -88,6 +88,8 @@ The dual space of an $R$-module $M$ is the $R$-module of $R$-linear maps $M \to
 Erdős-Kaplansky theorem about the dimension of a dual vector space in case of infinite dimension.
 -/
 
+set_option autoImplicit true
+
 
 noncomputable section
 

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -215,7 +215,7 @@ theorem LinearMap.dualMap_id : (LinearMap.id : M₁ →ₗ[R] M₁).dualMap = Li
   rfl
 #align linear_map.dual_map_id LinearMap.dualMap_id
 
-theorem LinearMap.dualMap_comp_dualMap {M₃ : Type _} [AddCommGroup M₃] [Module R M₃]
+theorem LinearMap.dualMap_comp_dualMap {M₃ : Type*} [AddCommGroup M₃] [Module R M₃]
     (f : M₁ →ₗ[R] M₂) (g : M₂ →ₗ[R] M₃) : f.dualMap.comp g.dualMap = (g.comp f).dualMap :=
   rfl
 #align linear_map.dual_map_comp_dual_map LinearMap.dualMap_comp_dualMap
@@ -262,7 +262,7 @@ theorem LinearEquiv.dualMap_symm {f : M₁ ≃ₗ[R] M₂} :
   rfl
 #align linear_equiv.dual_map_symm LinearEquiv.dualMap_symm
 
-theorem LinearEquiv.dualMap_trans {M₃ : Type _} [AddCommGroup M₃] [Module R M₃] (f : M₁ ≃ₗ[R] M₂)
+theorem LinearEquiv.dualMap_trans {M₃ : Type*} [AddCommGroup M₃] [Module R M₃] (f : M₁ ≃ₗ[R] M₂)
     (g : M₂ ≃ₗ[R] M₃) : g.dualMap.trans f.dualMap = (f.trans g).dualMap :=
   rfl
 #align linear_equiv.dual_map_trans LinearEquiv.dualMap_trans
@@ -459,7 +459,7 @@ theorem dualBasis_equivFun [Fintype ι] (l : Dual R M) (i : ι) :
     b.dualBasis.equivFun l i = l (b i) := by rw [Basis.equivFun_apply, dualBasis_repr]
 #align basis.dual_basis_equiv_fun Basis.dualBasis_equivFun
 
-theorem eval_ker {ι : Type _} (b : Basis ι R M) :
+theorem eval_ker {ι : Type*} (b : Basis ι R M) :
     LinearMap.ker (Dual.eval R M) = ⊥ := by
   rw [ker_eq_bot']
   intro m hm
@@ -468,7 +468,7 @@ theorem eval_ker {ι : Type _} (b : Basis ι R M) :
 #align basis.eval_ker Basis.eval_ker
 
 -- Porting note: broken dot notation lean4#1910 LinearMap.range
-theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) :
+theorem eval_range {ι : Type*} [Finite ι] (b : Basis ι R M) :
     LinearMap.range (Dual.eval R M) = ⊤ := by
   classical
     cases nonempty_fintype ι
@@ -578,7 +578,7 @@ section IsReflexive
 
 open Function
 
-variable (R M : Type _) [CommRing R] [AddCommGroup M] [Module R M]
+variable (R M : Type*) [CommRing R] [AddCommGroup M] [Module R M]
 
 /-- A reflexive module is one for which the natural map to its double dual is a bijection.
 
@@ -638,7 +638,7 @@ theorem mapEvalEquiv_symm_apply (W'' : Submodule R (Dual R (Dual R M))) :
 #align module.map_eval_equiv_symm_apply Module.mapEvalEquiv_symm_apply
 
 instance _root_.Prod.instModuleIsReflexive
-    {N : Type _} [AddCommGroup N] [Module R N] [IsReflexive R N] :
+    {N : Type*} [AddCommGroup N] [Module R N] [IsReflexive R N] :
     IsReflexive R (M × N) where
   bijective_dual_eval' := by
     let e : Dual R (Dual R (M × N)) ≃ₗ[R] Dual R (Dual R M) × Dual R (Dual R N) :=
@@ -672,7 +672,7 @@ section DualBases
 
 open Module
 
-variable {R M ι : Type _}
+variable {R M ι : Type*}
 
 variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
 
@@ -699,7 +699,7 @@ namespace Module.DualBases
 
 open Module Module.Dual LinearMap Function
 
-variable {R M ι : Type _}
+variable {R M ι : Type*}
 
 variable [CommRing R] [AddCommGroup M] [Module R M]
 
@@ -865,7 +865,7 @@ theorem mem_dualCoannihilator {Φ : Submodule R (Module.Dual R M)} (x : M) :
   simp_rw [dualCoannihilator, mem_comap, mem_dualAnnihilator, Module.Dual.eval_apply]
 #align submodule.mem_dual_coannihilator Submodule.mem_dualCoannihilator
 
-theorem dualAnnihilator_gc (R M : Type _) [CommSemiring R] [AddCommMonoid M] [Module R M] :
+theorem dualAnnihilator_gc (R M : Type*) [CommSemiring R] [AddCommMonoid M] [Module R M] :
     GaloisConnection
       (OrderDual.toDual ∘ (dualAnnihilator : Submodule R M → Submodule R (Module.Dual R M)))
       (dualCoannihilator ∘ OrderDual.ofDual) := by
@@ -946,12 +946,12 @@ theorem dualCoannihilator_sup_eq (U V : Submodule R (Module.Dual R M)) :
   (dualAnnihilator_gc R M).u_inf
 #align submodule.dual_coannihilator_sup_eq Submodule.dualCoannihilator_sup_eq
 
-theorem dualAnnihilator_iSup_eq {ι : Type _} (U : ι → Submodule R M) :
+theorem dualAnnihilator_iSup_eq {ι : Type*} (U : ι → Submodule R M) :
     (⨆ i : ι, U i).dualAnnihilator = ⨅ i : ι, (U i).dualAnnihilator :=
   (dualAnnihilator_gc R M).l_iSup
 #align submodule.dual_annihilator_supr_eq Submodule.dualAnnihilator_iSup_eq
 
-theorem dualCoannihilator_iSup_eq {ι : Type _} (U : ι → Submodule R (Module.Dual R M)) :
+theorem dualCoannihilator_iSup_eq {ι : Type*} (U : ι → Submodule R (Module.Dual R M)) :
     (⨆ i : ι, U i).dualCoannihilator = ⨅ i : ι, (U i).dualCoannihilator :=
   (dualAnnihilator_gc R M).u_iInf
 #align submodule.dual_coannihilator_supr_eq Submodule.dualCoannihilator_iSup_eq
@@ -964,7 +964,7 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
 #align submodule.sup_dual_annihilator_le_inf Submodule.sup_dualAnnihilator_le_inf
 
 /-- See also `Subspace.dualAnnihilator_iInf_eq` for vector subspaces when `ι` is finite. -/
-theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
+theorem iSup_dualAnnihilator_le_iInf {ι : Type*} (U : ι → Submodule R M) :
     ⨆ i : ι, (U i).dualAnnihilator ≤ (⨅ i : ι, U i).dualAnnihilator := by
   rw [le_dualAnnihilator_iff_le_dualCoannihilator, dualCoannihilator_iSup_eq]
   apply iInf_mono
@@ -1021,7 +1021,7 @@ theorem forall_mem_dualAnnihilator_apply_eq_zero_iff (W : Subspace K V) (v : V)
 #align subspace.forall_mem_dual_annihilator_apply_eq_zero_iff Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff
 
 /-- `Submodule.dualAnnihilator` and `Submodule.dualCoannihilator` form a Galois coinsertion. -/
-def dualAnnihilatorGci (K V : Type _) [Field K] [AddCommGroup V] [Module K V] :
+def dualAnnihilatorGci (K V : Type*) [Field K] [AddCommGroup V] [Module K V] :
     GaloisCoinsertion
       (OrderDual.toDual ∘ (dualAnnihilator : Subspace K V → Subspace K (Module.Dual K V)))
       (dualCoannihilator ∘ OrderDual.ofDual) where
@@ -1127,7 +1127,7 @@ section
 
 open FiniteDimensional
 
-variable {V₁ : Type _} [AddCommGroup V₁] [Module K V₁]
+variable {V₁ : Type*} [AddCommGroup V₁] [Module K V₁]
 
 instance instModuleDualFiniteDimensional [H : FiniteDimensional K V] :
     FiniteDimensional K (Module.Dual K V) := by
@@ -1229,7 +1229,7 @@ end LinearMap
 
 section CommRing
 
-variable {R M M' : Type _}
+variable {R M M' : Type*}
 
 variable [CommRing R] [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M']
 
@@ -1477,7 +1477,7 @@ theorem dualAnnihilator_inf_eq (W W' : Subspace K V₁) :
 -- for `Module.Dual R (Π (i : ι), V ⧸ W i) ≃ₗ[K] Π (i : ι), Module.Dual R (V ⧸ W i)`, which is not
 -- true for infinite `ι`. One would need to add additional hypothesis on `W` (for example, it might
 -- be true when the family is inf-closed).
-theorem dualAnnihilator_iInf_eq {ι : Type _} [Finite ι] (W : ι → Subspace K V₁) :
+theorem dualAnnihilator_iInf_eq {ι : Type*} [Finite ι] (W : ι → Subspace K V₁) :
     (⨅ i : ι, W i).dualAnnihilator = ⨆ i : ι, (W i).dualAnnihilator := by
   revert ι
   refine' @Finite.induction_empty_option _ _ _ _
@@ -1564,9 +1564,9 @@ end VectorSpace
 
 namespace TensorProduct
 
-variable (R : Type _) (M : Type _) (N : Type _)
+variable (R : Type*) (M : Type*) (N : Type*)
 
-variable {ι κ : Type _}
+variable {ι κ : Type*}
 
 variable [DecidableEq ι] [DecidableEq κ]
 

This also changes basisFintypeOfFiniteSpans to use Finite rather than Fintype, as it was noncomputable anyway. This means it has to be renamed to basis_finite_of_finite_spans as it now is a proof!

Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -477,7 +477,7 @@ theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) :
 
 section
 
-variable [Finite R M] [Free R M] [Nontrivial R]
+variable [Finite R M] [Free R M]
 
 instance dual_free : Free R (Dual R M) :=
   Free.of_basis (Free.chooseBasis R M).dualBasis
@@ -516,7 +516,7 @@ namespace Module
 
 variable {K : Type u₁} {V : Type u₂}
 
-variable [Field K] [AddCommGroup V] [Module K V]
+variable [CommRing K] [AddCommGroup V] [Module K V] [Module.Free K V]
 
 open Module Module.Dual Submodule LinearMap Cardinal Basis FiniteDimensional
 
@@ -526,7 +526,7 @@ variable (K) (V)
 
 -- Porting note: broken dot notation lean4#1910 LinearMap.ker
 theorem eval_ker : LinearMap.ker (eval K V) = ⊥ := by
-  classical exact (Basis.ofVectorSpace K V).eval_ker
+  classical exact (Module.Free.chooseBasis K V).eval_ker
 #align module.eval_ker Module.eval_ker
 
 theorem map_eval_injective : (Submodule.map (eval K V)).Injective := by
@@ -564,16 +564,14 @@ theorem forall_dual_apply_eq_zero_iff (v : V) : (∀ φ : Module.Dual K V, φ v
 
 end
 
--- TODO(jmc): generalize to rings, once `Module.rank` is generalized
-theorem dual_rank_eq [FiniteDimensional K V] :
+theorem dual_rank_eq [Module.Finite K V] :
     Cardinal.lift.{u₁,u₂} (Module.rank K V) = Module.rank K (Dual K V) :=
-  (Basis.ofVectorSpace K V).dual_rank_eq
+  (Module.Free.chooseBasis K V).dual_rank_eq
 #align module.dual_rank_eq Module.dual_rank_eq
 
 -- Porting note: broken dot notation lean4#1910 LinearMap.range
-theorem erange_coe [FiniteDimensional K V] : LinearMap.range (eval K V) = ⊤ :=
-  letI : IsNoetherian K V := IsNoetherian.iff_fg.2 inferInstance
-  (Basis.ofVectorSpace K V).eval_range
+theorem erange_coe [Module.Finite K V] : LinearMap.range (eval K V) = ⊤ :=
+  (Module.Free.chooseBasis K V).eval_range
 #align module.erange_coe Module.erange_coe
 
 section IsReflexive
@@ -593,12 +591,9 @@ class IsReflexive : Prop where
 lemma bijective_dual_eval [IsReflexive R M] : Bijective $ Dual.eval R M :=
   IsReflexive.bijective_dual_eval'
 
-instance IsReflexive.of_finite_of_free [Finite R M] [Free R M] : IsReflexive R M := by
-  cases' h : subsingleton_or_nontrivial R
-  · have := Module.subsingleton R M
-    exact ⟨⟨fun x y _ ↦ by simp, fun x ↦ ⟨0, by simp⟩⟩⟩
-  · exact ⟨⟨LinearMap.ker_eq_bot.mp (Free.chooseBasis R M).eval_ker,
-            LinearMap.range_eq_top.mp (Free.chooseBasis R M).eval_range⟩⟩
+instance IsReflexive.of_finite_of_free [Finite R M] [Free R M] : IsReflexive R M where
+  bijective_dual_eval' := ⟨LinearMap.ker_eq_bot.mp (Free.chooseBasis R M).eval_ker,
+                           LinearMap.range_eq_top.mp (Free.chooseBasis R M).eval_range⟩
 
 variable [IsReflexive R M]
 
@@ -1675,8 +1670,6 @@ variable (R M N)
 
 variable [Module.Finite R M] [Module.Finite R N] [Module.Free R M] [Module.Free R N]
 
-variable [Nontrivial R]
-
 /--
 A linear equivalence between `Dual M ⊗ Dual N` and `Dual (M ⊗ N)` when `M` and `N` are finite free
 modules. It sends `f ⊗ g` to the composition of `TensorProduct.map f g` with the natural

The lemma is a perfect duplicate of Submodule.eq_top_of_finrank_eq.

@@ -1547,7 +1547,7 @@ theorem dualMap_injective_iff {f : V₁ →ₗ[K] V₂} :
   refine' ⟨_, fun h => dualMap_injective_of_surjective h⟩
   rw [← range_eq_top, ← ker_eq_bot]
   intro h
-  apply FiniteDimensional.eq_top_of_finrank_eq
+  apply Submodule.eq_top_of_finrank_eq
   rw [← finrank_eq_zero] at h
   rw [← add_zero (FiniteDimensional.finrank K <| LinearMap.range f), ← h, ←
     LinearMap.finrank_range_dualMap_eq_finrank_range, LinearMap.finrank_range_add_finrank_ker,

This uncovers a few situations where a lemma was stated with the wrong decidability assumption. The corrected lemmas are strictly more syntactically-general.

This is exhaustive in the LinearAlgebra folder.

Where removal is impractical, this switches to open Classical in to make the intent clear.

@@ -477,8 +477,6 @@ theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) :
 
 section
 
-open Classical
-
 variable [Finite R M] [Free R M] [Nontrivial R]
 
 instance dual_free : Free R (Dual R M) :=
@@ -1132,8 +1130,6 @@ theorem dualEquivDual_apply (φ : Module.Dual K W) :
 
 section
 
-open Classical
-
 open FiniteDimensional
 
 variable {V₁ : Type _} [AddCommGroup V₁] [Module K V₁]
@@ -1154,8 +1150,9 @@ theorem dualAnnihilator_dualAnnihilator_eq (W : Subspace K V) :
 
 -- TODO(kmill): https://github.com/leanprover-community/mathlib/pull/17521#discussion_r1083241963
 @[simp]
-theorem dual_finrank_eq : finrank K (Module.Dual K V) = finrank K V :=
-  LinearEquiv.finrank_eq (Basis.ofVectorSpace K V).toDualEquiv.symm
+theorem dual_finrank_eq : finrank K (Module.Dual K V) = finrank K V := by
+  classical
+  exact LinearEquiv.finrank_eq (Basis.ofVectorSpace K V).toDualEquiv.symm
 #align subspace.dual_finrank_eq Subspace.dual_finrank_eq
 
 /-- The quotient by the dual is isomorphic to its dual annihilator.  -/
@@ -1165,6 +1162,7 @@ noncomputable def quotDualEquivAnnihilator (W : Subspace K V) :
   LinearEquiv.quotEquivOfQuotEquiv <| LinearEquiv.trans W.quotAnnihilatorEquiv W.dualEquivDual
 #align subspace.quot_dual_equiv_annihilator Subspace.quotDualEquivAnnihilator
 
+open scoped Classical in
 /-- The quotient by a subspace is isomorphic to its dual annihilator. -/
 noncomputable def quotEquivAnnihilator (W : Subspace K V) : (V ⧸ W) ≃ₗ[K] W.dualAnnihilator :=
   let φ := (Basis.ofVectorSpace K W).toDualEquiv.trans W.dualEquivDual
@@ -1679,8 +1677,6 @@ variable [Module.Finite R M] [Module.Finite R N] [Module.Free R M] [Module.Free
 
 variable [Nontrivial R]
 
-open Classical
-
 /--
 A linear equivalence between `Dual M ⊗ Dual N` and `Dual (M ⊗ N)` when `M` and `N` are finite free
 modules. It sends `f ⊗ g` to the composition of `TensorProduct.map f g` with the natural

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -475,17 +475,6 @@ theorem eval_range {ι : Type _} [Finite ι] (b : Basis ι R M) :
     rw [← b.toDual_toDual, range_comp, b.toDual_range, Submodule.map_top, toDual_range _]
 #align basis.eval_range Basis.eval_range
 
-/-- A module with a basis is linearly equivalent to the dual of its dual space. -/
-def evalEquiv {ι : Type _} [Finite ι] (b : Basis ι R M) : M ≃ₗ[R] Dual R (Dual R M) :=
-  LinearEquiv.ofBijective (eval R M) ⟨ker_eq_bot.mp b.eval_ker, range_eq_top.mp b.eval_range⟩
-#align basis.eval_equiv Basis.evalEquiv
-
-@[simp]
-theorem evalEquiv_toLinearMap {ι : Type _} [Finite ι] (b : Basis ι R M) :
-    b.evalEquiv.toLinearMap = Dual.eval R M :=
-  rfl
-#align basis.eval_equiv_to_linear_map Basis.evalEquiv_toLinearMap
-
 section
 
 open Classical
@@ -589,42 +578,101 @@ theorem erange_coe [FiniteDimensional K V] : LinearMap.range (eval K V) = ⊤ :=
   (Basis.ofVectorSpace K V).eval_range
 #align module.erange_coe Module.erange_coe
 
-variable (K V)
+section IsReflexive
 
-/-- A vector space is linearly equivalent to the dual of its dual space. -/
-def evalEquiv [FiniteDimensional K V] : V ≃ₗ[K] Dual K (Dual K V) :=
-  LinearEquiv.ofBijective
-    (eval K V)-- 60x faster elaboration than using `ker_eq_bot.mp eval_ker` directly:
-    ⟨by
-      rw [← ker_eq_bot]
-      apply eval_ker K V, range_eq_top.mp erange_coe⟩
-#align module.eval_equiv Module.evalEquiv
+open Function
 
-/-- The isomorphism `Module.evalEquiv` induces an order isomorphism on subspaces. -/
-def mapEvalEquiv [FiniteDimensional K V] : Subspace K V ≃o Subspace K (Dual K (Dual K V)) :=
-  Submodule.orderIsoMapComap (evalEquiv K V)
-#align module.map_eval_equiv Module.mapEvalEquiv
+variable (R M : Type _) [CommRing R] [AddCommGroup M] [Module R M]
 
-variable {K V}
+/-- A reflexive module is one for which the natural map to its double dual is a bijection.
 
-@[simp]
-theorem evalEquiv_toLinearMap [FiniteDimensional K V] :
-    (evalEquiv K V).toLinearMap = Dual.eval K V :=
-  rfl
+Any finitely-generated free module (and thus any finite-dimensional vector space) is reflexive.
+See `Module.IsReflexive.of_finite_of_free`. -/
+class IsReflexive : Prop where
+  /-- A reflexive module is one for which the natural map to its double dual is a bijection. -/
+  bijective_dual_eval' : Bijective $ Dual.eval R M
+
+lemma bijective_dual_eval [IsReflexive R M] : Bijective $ Dual.eval R M :=
+  IsReflexive.bijective_dual_eval'
+
+instance IsReflexive.of_finite_of_free [Finite R M] [Free R M] : IsReflexive R M := by
+  cases' h : subsingleton_or_nontrivial R
+  · have := Module.subsingleton R M
+    exact ⟨⟨fun x y _ ↦ by simp, fun x ↦ ⟨0, by simp⟩⟩⟩
+  · exact ⟨⟨LinearMap.ker_eq_bot.mp (Free.chooseBasis R M).eval_ker,
+            LinearMap.range_eq_top.mp (Free.chooseBasis R M).eval_range⟩⟩
+
+variable [IsReflexive R M]
+
+/-- The bijection between a reflexive module and its double dual, bundled as a `LinearEquiv`. -/
+def evalEquiv : M ≃ₗ[R] Dual R (Dual R M) :=
+  LinearEquiv.ofBijective _ $ bijective_dual_eval R M
+#align module.eval_equiv Module.evalEquiv
+
+@[simp] lemma evalEquiv_toLinearMap : evalEquiv R M = Dual.eval R M := rfl
 #align module.eval_equiv_to_linear_map Module.evalEquiv_toLinearMap
 
+@[simp] lemma evalEquiv_apply (m : M) : evalEquiv R M m = Dual.eval R M m := rfl
+
+@[simp] lemma apply_evalEquiv_symm_apply (f : Dual R M) (g : Dual R $ Dual R M) :
+    f ((evalEquiv R M).symm g) = g f := by
+  set m := (evalEquiv R M).symm g
+  rw [← (evalEquiv R M).apply_symm_apply g, evalEquiv_apply, Dual.eval_apply]
+
+@[simp] lemma symm_dualMap_evalEquiv :
+    (evalEquiv R M).symm.dualMap = Dual.eval R (Dual R M) := by
+  ext; simp
+
+/-- The dual of a reflexive module is reflexive. -/
+instance Dual.instIsReflecive : IsReflexive R (Dual R M) :=
+⟨by simpa only [← symm_dualMap_evalEquiv] using (evalEquiv R M).dualMap.symm.bijective⟩
+
+/-- The isomorphism `Module.evalEquiv` induces an order isomorphism on subspaces. -/
+def mapEvalEquiv : Submodule R M ≃o Submodule R (Dual R (Dual R M)) :=
+  Submodule.orderIsoMapComap (evalEquiv R M)
+#align module.map_eval_equiv Module.mapEvalEquiv
+
 @[simp]
-theorem mapEvalEquiv_apply [FiniteDimensional K V] (W : Subspace K V) :
-    mapEvalEquiv K V W = W.map (eval K V) :=
+theorem mapEvalEquiv_apply (W : Submodule R M) :
+    mapEvalEquiv R M W = W.map (Dual.eval R M) :=
   rfl
 #align module.map_eval_equiv_apply Module.mapEvalEquiv_apply
 
 @[simp]
-theorem mapEvalEquiv_symm_apply [FiniteDimensional K V] (W'' : Subspace K (Dual K (Dual K V))) :
-    (mapEvalEquiv K V).symm W'' = W''.comap (eval K V) :=
+theorem mapEvalEquiv_symm_apply (W'' : Submodule R (Dual R (Dual R M))) :
+    (mapEvalEquiv R M).symm W'' = W''.comap (Dual.eval R M) :=
   rfl
 #align module.map_eval_equiv_symm_apply Module.mapEvalEquiv_symm_apply
 
+instance _root_.Prod.instModuleIsReflexive
+    {N : Type _} [AddCommGroup N] [Module R N] [IsReflexive R N] :
+    IsReflexive R (M × N) where
+  bijective_dual_eval' := by
+    let e : Dual R (Dual R (M × N)) ≃ₗ[R] Dual R (Dual R M) × Dual R (Dual R N) :=
+      (dualProdDualEquivDual R M N).dualMap.trans
+        (dualProdDualEquivDual R (Dual R M) (Dual R N)).symm
+    have : Dual.eval R (M × N) = e.symm.comp ((Dual.eval R M).prodMap (Dual.eval R N)) := by
+      ext m f <;> simp
+    simp only [this, LinearEquiv.trans_symm, LinearEquiv.symm_symm, LinearEquiv.dualMap_symm,
+      coe_comp, LinearEquiv.coe_coe, EquivLike.comp_bijective]
+    exact Bijective.Prod_map (bijective_dual_eval R M) (bijective_dual_eval R N)
+
+instance _root_.MulOpposite.instModuleIsReflexive : IsReflexive R (MulOpposite M) where
+  bijective_dual_eval' := by
+    let e : Dual R (Dual R (MulOpposite M)) ≃ₗ[R] Dual R (Dual R M) :=
+      LinearEquiv.dualMap <| LinearEquiv.dualMap <| MulOpposite.opLinearEquiv _ |>.symm
+    have : Dual.eval R (MulOpposite M) = e.symm.comp ((Dual.eval R M).comp
+        <| MulOpposite.opLinearEquiv _ |>.symm.toLinearMap) := by
+      ext m f; rfl
+    simp only [this, LinearEquiv.trans_symm, LinearEquiv.symm_symm, LinearEquiv.dualMap_symm,
+      coe_comp, LinearEquiv.coe_coe, EquivLike.comp_bijective]
+    refine Bijective.comp (bijective_dual_eval R M) (LinearEquiv.bijective _)
+
+-- TODO: add `ULift.instModuleIsReflexive : IsReflexive R (ULift.{v} M)` once we have
+-- `LinearEquiv.ulift`
+
+end IsReflexive
+
 end Module
 
 section DualBases

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
-
-! This file was ported from Lean 3 source module linear_algebra.dual
-! leanprover-community/mathlib commit b1c017582e9f18d8494e5c18602a8cb4a6f843ac
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.FiniteDimensional
 import Mathlib.LinearAlgebra.Projection
@@ -14,6 +9,8 @@ import Mathlib.LinearAlgebra.SesquilinearForm
 import Mathlib.RingTheory.Finiteness
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 
+#align_import linear_algebra.dual from "leanprover-community/mathlib"@"b1c017582e9f18d8494e5c18602a8cb4a6f843ac"
+
 /-!
 # Dual vector spaces
 

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -1624,8 +1624,8 @@ isomorphism `R ⊗ R ≃ R`.
 noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N) :
     Dual R M ⊗[R] Dual R N ≃ₗ[R] Dual R (M ⊗[R] N) := by
   refine' LinearEquiv.ofLinear (dualDistrib R M N) (dualDistribInvOfBasis b c) _ _
-  . exact dualDistrib_dualDistribInvOfBasis_left_inverse _ _
-  . exact dualDistrib_dualDistribInvOfBasis_right_inverse _ _
+  · exact dualDistrib_dualDistribInvOfBasis_left_inverse _ _
+  · exact dualDistrib_dualDistribInvOfBasis_right_inverse _ _
 #align tensor_product.dual_distrib_equiv_of_basis TensorProduct.dualDistribEquivOfBasis
 
 variable (R M N)

@@ -927,7 +927,7 @@ theorem sup_dualAnnihilator_le_inf (U V : Submodule R M) :
 
 /-- See also `Subspace.dualAnnihilator_iInf_eq` for vector subspaces when `ι` is finite. -/
 theorem iSup_dualAnnihilator_le_iInf {ι : Type _} (U : ι → Submodule R M) :
-    (⨆ i : ι, (U i).dualAnnihilator) ≤ (⨅ i : ι, U i).dualAnnihilator := by
+    ⨆ i : ι, (U i).dualAnnihilator ≤ (⨅ i : ι, U i).dualAnnihilator := by
   rw [le_dualAnnihilator_iff_le_dualCoannihilator, dualCoannihilator_iSup_eq]
   apply iInf_mono
   exact fun i : ι => le_dualAnnihilator_dualCoannihilator (U i)

Sets new records for set_option maxHeartbeats. :-( I spent too long struggling with this one; if anyone would like to take another look please do.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -1093,7 +1093,10 @@ open FiniteDimensional
 
 variable {V₁ : Type _} [AddCommGroup V₁] [Module K V₁]
 
-instance [H : FiniteDimensional K V] : FiniteDimensional K (Module.Dual K V) := by infer_instance
+instance instModuleDualFiniteDimensional [H : FiniteDimensional K V] :
+    FiniteDimensional K (Module.Dual K V) := by
+  infer_instance
+#align subspace.module.dual.finite_dimensional Subspace.instModuleDualFiniteDimensional
 
 variable [FiniteDimensional K V] [FiniteDimensional K V₁]
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -966,7 +966,7 @@ theorem dualAnnihilator_dualCoannihilator_eq {W : Subspace K V} :
     rintro rfl
     exact hw'n (Submodule.zero_mem W)
   rw [Ne.def, ← Module.forall_dual_apply_eq_zero_iff K w'] at hw'nz
-  push_neg  at hw'nz
+  push_neg at hw'nz
   obtain ⟨φ, hφ⟩ := hw'nz
   exists ((LinearMap.ofIsComplProd hW).comp (LinearMap.inr _ _ _)) φ
   simp only [coe_comp, coe_inr, Function.comp_apply, ofIsComplProd_apply, map_add,
@@ -1452,7 +1452,7 @@ theorem dualAnnihilator_iInf_eq {ι : Type _} [Finite ι] (W : ι → Subspace K
 to direct sum decompositions. -/
 theorem isCompl_dualAnnihilator {W W' : Subspace K V₁} (h : IsCompl W W') :
     IsCompl W.dualAnnihilator W'.dualAnnihilator := by
-  rw [isCompl_iff, disjoint_iff, codisjoint_iff] at h⊢
+  rw [isCompl_iff, disjoint_iff, codisjoint_iff] at h ⊢
   rw [← dualAnnihilator_inf_eq, ← dualAnnihilator_sup_eq, h.1, h.2, dualAnnihilator_top,
     dualAnnihilator_bot]
   exact ⟨rfl, rfl⟩

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -445,7 +445,7 @@ theorem dualBasis_apply (i : ι) (m : M) : b.dualBasis i m = b.repr m i :=
 
 @[simp]
 theorem coe_dualBasis : ⇑b.dualBasis = b.coord := by
-  ext (i x)
+  ext i x
   apply dualBasis_apply
 #align basis.coe_dual_basis Basis.coe_dualBasis
 
@@ -1028,7 +1028,7 @@ theorem dualLift_of_mem {φ : Module.Dual K W} {w : V} (hw : w ∈ W) : W.dualLi
 
 @[simp]
 theorem dualRestrict_comp_dualLift (W : Subspace K V) : W.dualRestrict.comp W.dualLift = 1 := by
-  ext (φ x)
+  ext φ x
   simp
 #align subspace.dual_restrict_comp_dual_lift Subspace.dualRestrict_comp_dualLift
 
@@ -1303,7 +1303,7 @@ theorem range_dualMap_eq_dualAnnihilator_ker_of_surjective (f : M →ₗ[R] M')
   · rw [LinearMap.range_comp_of_range_eq_top]
     apply LinearEquiv.range
   · apply congr_arg
-    ext (φ x)
+    ext φ x
     simp only [LinearMap.coe_comp, LinearEquiv.coe_toLinearMap, LinearMap.dualMap_apply,
       LinearEquiv.dualMap_apply, mkQ_apply, LinearMap.quotKerEquivOfSurjective,
       LinearEquiv.trans_symm, LinearEquiv.trans_apply, LinearEquiv.ofTop_symm_apply,

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -642,7 +642,7 @@ variable [CommSemiring R] [AddCommMonoid M] [Module R M] [DecidableEq ι]
 open Lean.Elab.Tactic in
 /-- Try using `Set.to_finite` to dispatch a `Set.finite` goal. -/
 def evalUseFiniteInstance : TacticM Unit := do
-  evalTactic (← `(tactic|intros; apply Set.toFinite ))
+  evalTactic (← `(tactic| intros; apply Set.toFinite ))
 
 elab "use_finite_instance" : tactic => evalUseFiniteInstance
 
@@ -811,7 +811,7 @@ theorem mem_dualAnnihilator (φ : Module.Dual R M) : φ ∈ W.dualAnnihilator 
 /-- That $\operatorname{ker}(\iota^* : V^* \to W^*) = \operatorname{ann}(W)$.
 This is the definition of the dual annihilator of the submodule $W$. -/
 theorem dualRestrict_ker_eq_dualAnnihilator (W : Submodule R M) :
--- Porting note: broken dot notation lean4#1910 LinearMap.ker
+    -- Porting note: broken dot notation lean4#1910 LinearMap.ker
     LinearMap.ker W.dualRestrict = W.dualAnnihilator :=
   rfl
 #align submodule.dual_restrict_ker_eq_dual_annihilator Submodule.dualRestrict_ker_eq_dualAnnihilator
@@ -1644,4 +1644,3 @@ noncomputable def dualDistribEquiv : Dual R M ⊗[R] Dual R N ≃ₗ[R] Dual R (
 #align tensor_product.dual_distrib_equiv TensorProduct.dualDistribEquiv
 
 end TensorProduct
-

These are all doc fixes

@@ -1140,7 +1140,7 @@ theorem finrank_dualCoannihilator_eq {Φ : Subspace K (Module.Dual K V)} :
 theorem finrank_add_finrank_dualCoannihilator_eq (W : Subspace K (Module.Dual K V)) :
     finrank K W + finrank K W.dualCoannihilator = finrank K V := by
   rw [finrank_dualCoannihilator_eq]
-  -- Porting note: LineqrEquiv.finrank_eq needs help
+  -- Porting note: LinearEquiv.finrank_eq needs help
   let equiv := W.quotEquivAnnihilator
   have eq := LinearEquiv.finrank_eq (R := K) (M := (Module.Dual K V) ⧸ W)
     (M₂ := { x // x ∈ dualAnnihilator W }) equiv
@@ -1575,7 +1575,7 @@ variable [Module R M] [Module R N]
 -/
 noncomputable def dualDistribInvOfBasis (b : Basis ι R M) (c : Basis κ R N) :
     Dual R (M ⊗[R] N) →ₗ[R] Dual R M ⊗[R] Dual R N :=
-  -- Porting note: ∑ (i) (j) does not seem to work; applyₗneeds a little help to unify
+  -- Porting note: ∑ (i) (j) does not seem to work; applyₗ needs a little help to unify
   ∑ i, ∑ j,
     (ringLmapEquivSelf R ℕ _).symm (b.dualBasis i ⊗ₜ c.dualBasis j) ∘ₗ
       (applyₗ (R := R) (c j)) ∘ₗ (applyₗ (R := R) (b i)) ∘ₗ lcurry R M N R

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com>